# Expanding_brackets

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### Expanding and Simplifying Algebraic Expressions:

Expanding and Simplifying Algebraic Expressions Lesson Aims: To be able to simplify algebraic expressions To be able to expand a single bracket, including negative numbers

### Review of Algebraic Expressions:

Review of Algebraic Expressions So far we have learned that: 2c means 2 multiplied by c z means z divided by six. 6

### What is the value of this expression?:

What is the value of this expression? y 2 + 5 when y = 4

### What is the value of this expression?:

What is the value of this expression? y 2 + 5 when y = 4 (4 x 4) + 5 = 16 +5 = 21

### Is this true for any number? a + b = b + a (hint: does 4 + 3 = 3 + 4? Imagine that a and b are numbers. Does it matter what order we use to add them? :

Is this true for any number? a + b = b + a (hint: does 4 + 3 = 3 + 4? Imagine that a and b are numbers. Does it matter what order we use to add them?

### Is this true for any number? a - b = b - a (hint: does 7 - 5 = 5 - 7? Imagine that a and b are numbers. Does it matter what order we use to subtract them? :

Is this true for any number? a - b = b - a (hint: does 7 - 5 = 5 - 7? Imagine that a and b are numbers. Does it matter what order we use to subtract them?

### Simplifying Expressions:

Simplifying Expressions 2p + 4p = +

### Simplifying Expressions:

Simplifying Expressions 2p + 4p = So 2p + 4p = 6p + =

### Simplifying Expressions:

Simplifying Expressions 2a + 3a = +

### Simplifying Expressions:

Simplifying Expressions 2a + 3a = + = 2a +3a = 5a

### Simplifying Expressions:

Simplifying Expressions 2a + p = +

### Simplifying Expressions:

Simplifying Expressions We can only simplify when the terms have the same letter or variable. 2a + p = + = 2a + p

### Simplifying Expressions:

Simplifying Expressions 2a + p + 4a + 2k + 3p =

### Simplifying Expressions:

Simplifying Expressions 2a + p + 4a + 2k + 3p = First look at a: Then look at p: Then look at k:

### Simplifying Expressions:

Simplifying Expressions 2a + p + 4a + 2k + 3p = First look at a: 2a + 4a = 6a Then look at p: Then look at k:

### Simplifying Expressions:

Simplifying Expressions 2a + p + 4a + 2k + 3p = First look at a: 2a + 4a = 6a Then look at p: p + 3p = 4p Then look at k:

### Simplifying Expressions:

Simplifying Expressions 2a + p + 4a + 2k + 3p = First look at a: 2a + 4a = 6a Then look at p: p + 3p = 4p Then look at k: 2k

### Simplifying Expressions:

Simplifying Expressions 2a + p + 4a + 2k + 3p = First look at a: 2a + 4a = 6a Then look at p: p + 3p = 4p Then look at k: 2k So the expression becomes: 6a + 4p + 2k

### Expanding Brackets:

Expanding Brackets 3(a + 5) What does this mean? ‘add five to a then multiply the whole lot by three’ Or ‘three lots of a added to three lots of 5

### Expanding Brackets:

Expanding Brackets 3(a + 5) + 5 + 5 + 5 a a a

### Expanding Brackets:

Expanding Brackets 3(a + 5) + 5 + 5 + 5 a a a 3(a + 5) =

### Expanding Brackets:

Expanding Brackets 3(a + 5) + 5 + 5 + 5 a a a 3(a + 5) = (3 x a) +

### Expanding Brackets:

Expanding Brackets 3(a + 5) + 5 + 5 + 5 a a a 3(a + 5) = (3 x a) + (3 x 5) =

### Expanding Brackets:

Expanding Brackets 3(a + 5) + 5 + 5 + 5 a a a 3(a + 5) = (3 x a) + (3 x 5) = 3a + 15

### PowerPoint Presentation:

Expanding Brackets 6(2a + 4) + 4 + 4 + 4 6(2a + 4) = + 4 + 4 + 4 (6 x 2a) + (6 x 4) = 12a + 24

### Expanding Brackets:

Expanding Brackets Example: 5(2z – 3) Each term inside the brackets is multiplied by the number outside the brackets. Watch out for the signs!

### Expanding Brackets:

Expanding Brackets Example: 5(2z – 3) (5 x 2z) – 5 x 3

### Expanding Brackets:

Expanding Brackets Example: 5(2z – 3) (5 x 2z) – 5 x 3 = 10z – 15

### Expanding Brackets:

Expanding Brackets Example: 2(3p + 4) + 3(4p + 1)

### Expanding Brackets:

Expanding Brackets Example: 2(3p + 4) + 3(4p + 1) = (2 x 3p) + (2 x 4)

### Expanding Brackets:

Expanding Brackets Example: 2(3p + 4) + 3(4p + 1) = (2 x 3p) + (2 x 4) + (3 x 4p) + (3 x 1)

### Expanding Brackets:

Expanding Brackets Example: 2(3p + 4) + 3(4p + 1) = (2 x 3p) + (2 x 4) + (3 x 4p) + (3 x 1) = 6p + 8

### Expanding Brackets:

Expanding Brackets Example: 2(3p + 4) + 3(4p + 1) = (2 x 3p) + (2 x 4) + (3 x 4p) + (3 x 1) = 6p + 8 + 12p + 3

### Expanding Brackets:

Expanding Brackets Example: 2(3p + 4) + 3(4p + 1) = (2 x 3p) + (2 x 4) + (3 x 4p) + (3 x 1) = 6p + 8 + 12p + 3 = 18p + 11

### Solving with brackets:

Solving with brackets 3(2x+1) 2x + 1 2x + 1 2x + 1 How many x’s do I have in total? ______ What is the total value of my numbers? ___ 6x +3 3(2x+1) = 6x + 3

### Solving with brackets:

Solving with brackets 2(3a+2) 3a + 2 3a + 2 2 ( 3a +2 ) = 6a +4

### PowerPoint Presentation:

3 ( 3b +4 ) = 9b + 12 Remember: Write out the question. Multiply what is outside the bracket by the first thing inside the bracket. Multiply what is outside the bracket by the last thing inside the bracket.

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EXAMPLES EXPANDING BRACKETS 1) Expand the following brackets: (a) 6(a + b) (b) 5(2w – 4) (c) p(3q + 7) = (d) -3(x + y) (e) -(4x – 9) (f) -4(2d – 8e) (g) 5w + 3(w – 4m) (h) 2(3m – 4n) – 7n 6a + 6b = 10w - 20 = 3pq + 7p = -3x - 3y = -4x + 9 = -8d + 32e = 5w + 3w - 12m = 8w - 12m = 6m - 8n - 7n = 6m - 15n

### PowerPoint Presentation:

TASK 1 EXPANDING BRACKETS 1) Expand the following brackets: (a) 3(y + 1) = (b) 4(x + 2) = (c) 2(x – 6) = (d) 5(y – 9) = (e) 6(a + b) = (f) 3(f + d) = (g) 2(k – m) = (h) 6(j – p) = ( i ) 10(2x + y) = (j) 10(3a – 2b) = TASK 2 1) Match pairs and find the odd one out: 3y + 3 4x + 8 2x - 12 5y - 45 6a + 6b 3f + 3d 2k – 2m 6j – 6p 20x + 10y 30a – 20b

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TASK 3– NAUGHTS AND CROSSES GAME EXPANDING BRACKETS In pairs, create three of your own naughts and crosses grids on expanding brackets as shown below. Best out of three to win.

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TASK 4 Draw a 3 x 3 grid as shown below: Place any nine numbers below into the grid (repeats forbidden) EXPANDING BRACKETS

3(x+1)=3x+? 3

5(x+2)=?x+10 5

10(x+7)=10x+? 70

3(x+6)=3x+? 18

6(-7+x)=?+6x -42

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5(2x+11)=?x+55 10

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3(4x+10)=?x+30 12

?(x+2)=6x+12 6

?(2x+1)=4x+2 2

2(t-12)=2t+? -24

3(?x+3)=12x+9 4

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15 5d(3+2d)=?d+10d 2

5 ½ (6x+10)=3x+?

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7 EXPANDING BRACKETS 7(t-3)=?t-21

9 ?(4z-5)=36z-45

24 8(y+3)=8y+?

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More Expansion 1) Expand the following brackets: 5(p + q) (a) 9(m - n) (b) s(t + u) (c) 4(3d + 2) (d) a(2b + c) (e) 3(5j – 2k) (f) e(5 + 2f) (g) 10(13 – 5n) (h) 6(4g + 3h) (i) 8(a + b + c) (j) 2) Expand the following brackets: -(a + b) (a) -(q - p) (b) -(3p + 4) (c) -(7 – 2x) (d) -3(g + 2) (e) -2(d - f) (f) -5(2h + 3i) (g) -4(6d – 3f) (h) -3(-2j + k) (i) 3) Expand the following brackets: 4h + 5(2h + 3s) (c) 7(d + f) – 2d (b) 3w + 2(w + x) (a) 12x - 4(3y + 2x) (d) 2(2m – 3n) – 8n (e) 16p - 3(3q – 4p) (f) 5p + 5q 9m – 9n st + su 12d + 8 2ab + ac 15j – 6k 5e + 2ef 130 – 50n 24g + 18h 8a + 8b + 8c -a - b -q + p -3p - 4 -7 + 14x -3g - 6 -2d + 2f -10h – 15i -24d + 12f 6j – 3k = 3w + 2w + 2x = 5w + 2x = 7d + 7f – 2d = 5d + 7f = 4h + 10h + 15s = 14h + 15s = 12x – 12y - 8x = 4x – 12y = 4m – 6n – 8n = 4m – 14n = 16p – 9q + 12p = 28p – 9q

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x(x + 3) 2x(x + 2) 7(x + y) 7(4 + y) 12(x – 3) 5(x + 8) 2y(x + y) 3(1 – 2x) 18(x + 1 – y) z(z + 5) 3(3x + 3) 4(9 + x) 8(8x + 5) 4(3x + 4) 2(1 – x) 9(x) 8(2 + y) 2x(x + 5) 9(2x + 4) 3(x + 1) 17(2 + x) 2(x + 7) 12(x + 3) 4y(y + 1) x(x + 9) EXTENSION 1– CATCHPHRASE

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EXTENSION 2 (LEVEL 6) EXPANDING BRACKETS (a) y(y + 5) = (b) p(p – 4) = (c) b(b + c) = (d) q(2q + 4) = (e) t(2t – 3s) = (f) 2a(a + 3b) = (g) 2s(3s – 2t) = (h) 4q(2q + 3p) = ( i ) q 2 (3q + 2p) = (j) d 2 (4d - 2e) = 1) Expand the following brackets: y + 5y 2 p - 4p 2 b + bc 2 2q + 4q 2 2t - 3st 2 2a + 6ab 2 6s - 4st 2 8q + 12pq 2 3q + 2pq 3 2 4d - 2d e 3 2 2) Show that: a(b + c) + b(a + c) + c(a + b) always equals the same as 2(ab + bc + ac) a(b + c) + b(a + c) + c(a + b) = ab + ac + ab + bc + ac + bc = 2ab + 2bc + 2ac = 2(ab + bc + ac)

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MINI-PLENARY ACTIVITY – SPOT THE MISTAKE 1) 3(x + 6) = 3x + 6 2) 9(p + 4) = p + 36 3) 5(x² - 3) = 5x² - 15 4) c(c + 4) = c² + 4 + c 5) –3(x + 1) = -3x + 3 6) 6(x + 5) = 6x + 11 7) 8(w + 3) = w + 24 8) 2(x² - 4) = 2x² + 8 9) f(e + 4) = ef + 4e Find the mistakes:

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PLENARY ACTIVITY (BINGO) T H S E R M A T U S B S

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A F K P U B G L Q V C H M R W D I N S X E J O T Y

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Expand 2(x+5) 2x+10

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Expand 9(t+2) 9t+18

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Expand 6(2x+3) 12x + 18

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Expand 7(3x+2) 21x + 14

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Expand 5(6x-5) 30x - 25

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Expand 6( x+y ) 6x + 6y

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Expand 5(3d+3) 15d + 15

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Expand b(2c+d) 2bc + bd

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Expand 5(3j - 4m) 15j – 20m

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Expand -( w+y ) -w - y

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Expand -(8-2f) -8 + 2f

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Expand -3(4d-2) -12d + 6

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Expand 3( a+b+c ) 3a + 3b + 3c

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Expand m(n+8) mn + 8m

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Expand g(h+9) gh + 9g

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Expand -p(m+2) -pm - 2

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Expand y( t+m ) yt + ym

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Expand r(m-2d) mr – 2dr

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Expand y(y+7) y + 7y 2

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Expand e(e+9) e + 9e 2

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Expand w(w+11) w + 11w 2

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Expand r(r - 7) r - 7r 2

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Expand e(e - 12) e - 12e 2

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Expand q(q - 6) q - 6q 2

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Expand h(h – 3m) h - 3hm 2

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What have you learnt? In your brain, write or draw everything you can remember about expanding single brackets. It can be a skill or a reflection, or something else that might be prominent in your brain. Draw your brain What level are we working at? Where are we in our journey? SELF ASSESSMENT

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. How well do you understand the task? I don’t understand I nearly understand I fully understand Plenary Activity

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Plenary Activity On your post it notes… Think about how you can improve your work. WWW (What Went Well) EBI (Even Better If) 