logging in or signing up Special Products and Factoring danlester Download Post to : URL : Related Presentations : Let's Connect Share Add to Flag Embed Email Send to Blogs and Networks Add to Channel Copy embed code: Embed: Flash iPad Dynamic Copy Does not support media & animations Automatically changes to Flash or non-Flash embed WordPress Embed Customize Embed URL: Copy Thumbnail: Copy The presentation is successfully added In Your Favorites. Views: 657 Category: Education License: All Rights Reserved Like it (1) Dislike it (0) Added: July 23, 2012 This Presentation is Public Favorites: 1 Presentation Description A short course on special products and factoring usually given to high school or first year college students. Comments Posting comment... Premium member Presentation Transcript Special Products and Factoring: Special Products and FactoringSpecial Products: Special Products Product of a monomial and a binomial a(x + y) = ax + aySpecial Products: Special Products Binomial Square (a + b) 2 = a 2 + 2ab + b 2 (a - b) 2 = a 2 – 2ab + b 2 The product of a binomial square is called PERFECT SQUARE TRINOMIALSpecial Products: Special Products Binomial Square (a + b) 2 = a 2 + 2ab + b 2 (a - b) 2 = a 2 – 2ab + b 2 Ex. (2x + 3) 2 = (2x) 2 + 2(2x)(3) + 3 2 = 4x 2 + 12x + 9Special Products: Special Products Product of the Sum and difference of two terms (a - b)(a + b) = a 2 - b 2 The product of the sum and difference of two terms is called: DIFFERENCE OF TWO SQUARESSpecial Products: Special Products Binomial Cube (x + y) 3 = x 3 + 3x 2 y + 3xy 2 + y 3 (x - y) 3 = x 3 - 3x 2 y + 3xy 2 - y 3Factoring: Factoring Common monomial factor ax + ay = a(x + y) Ex. 3x 2 + 6 - common factor is 3 3(x 2 + 2)Factoring: Factoring Difference of two squares x 2 - y 2 = (x) 2 – (y) 2 = (x + y)(x – y) Ex. 9x 2 – 4 = (3x) 2 – (2) 2 = [(3x) + 2][(3x) – 2] = (3x + 2)(3x – 2)Factoring: Factoring Perfect square trinomial x 2 + 2xy + y 2 = (x + y) 2 = (x + y)(x + y) x 2 - 2xy + y 2 = (x – y) 2 = (x – y)(x – y) Characteristics of a perfect square trinomial: The first term x 2 is a perfect square The last term is also a perfect square The middle term 2xy is twice the product of x and y The sign of the middle term determines the sign of the binomialFactoring: Factoring Perfect square trinomial x 2 + 2xy + y 2 = (x + y) 2 = (x + y)(x + y) x 2 - 2xy + y 2 = (x – y) 2 = (x – y)(x – y) Ex. 9x 2 – 6xy + y 2 9x 2 = (3x) 2 ; (y) 2 2(3x)(y) = 6xy 9x 2 – 6xy + y 2 = (3x – y) 2Factoring: Factoring Sum and difference of cubes x 3 + y 3 = (x) 3 + (y) 3 = (x + y)(x 2 – xy + y 2 ) x 3 - y 3 = (x) 3 - (y) 3 = (x - y)(x 2 + xy + y 2 )Factoring: Factoring Factoring by grouping ax + ay + bx + by = (ax + ay) + ( bx + by) = a(x + y) + b(x + y) = (a + b)(x +y)Factoring: Factoring Factoring a general trinomial ax 2 + bx + c How to test whether a given trinomial is factorable: Obtain the product ac. List down the factor pairs of the product ac. Choose among the factor pairs of ac that pair that will give a sum equal to the middle term b. * If no such pair gives a sum equal to the middle term b, then it is not factorableFactoring: Factoring Factoring a general trinomial ax 2 + bx + c Ex. 6x 2 + 5x – 21 5xFactoring: Factoring Factoring a general trinomial ax 2 + bx + c Try: You do not have the permission to view this presentation. In order to view it, please contact the author of the presentation.