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Multiplying polynomials :Multiplying polynomials To see multiplication “in your head” click here.
FOIL METHOD FOIL
Multiplying in your head :Multiplying in your head Multiply x² + 3x – 2 by 2x² – x + 4 (x² + 3x – 2)(2x² – x + 4)
Multiplying in your head :Multiplying in your head (x² + 3x – 2)(2x² – x + 4) Start by multiplying the first terms in each bracket to give a term in x4 = 2x4
Multiplying in your head :Multiplying in your head (x² + 3x – 2)(2x² – x + 4) Now look for pairs of terms which multiply together to give a term in x³. There are two pairs. – x³ = 2x4
Multiplying in your head :Multiplying in your head (x² + 3x – 2) ( 2x² – x + 4) Now look for pairs of terms which multiply together to give a term in x³. There are two pairs. – x³ + 6x³ = 2x4
Multiplying in your head :Multiplying in your head (x² + 3x – 2)(2x² – x + 4) Now look for pairs of terms which multiply together to give a term in x². There are three pairs. – x³ + 6x³ + 4x² = 2x4
Multiplying in your head :Multiplying in your head (x² + 3x – 2)(2x² – x + 4) Now look for pairs of terms which multiply together to give a term in x². There are three pairs. – x³ + 6x³ + 4x² = 2x4 - 3x²
Multiplying in your head :Multiplying in your head (x² + 3x – 2)(2x² – x + 4) Now look for pairs of terms which multiply together to give a term in x². There are three pairs. – x³ + 6x³ + 4x² - 3x² - 4x² = 2x4
Multiplying in your head :Multiplying in your head (x² + 3x – 2)(2x² – x + 4) Now look for pairs of terms which multiply together to give a term in x. There are two pairs. = 2x4 – x³ + 6x³ + 4x² - 3x² - 4x² + 12x
Multiplying in your head :Multiplying in your head (x² + 3x – 2)(2x² – x + 4) Now look for pairs of terms which multiply together to give a term in x. There are two pairs. = 2x4 – x³ + 6x³ + 4x² - 3x² - 4x² + 12x + 2x
Multiplying in your head :Multiplying in your head (x² + 3x – 2)(2x² – x + 4) Finally multiply the last two terms in each bracket to give the constant term. = 2x4 – x³ + 6x³ + 4x² - 3x² - 4x² + 12x + 2x - 8
Multiplying in your head :Multiplying in your head (x² + 3x – 2)(2x² – x + 4) Now simplify by collecting like terms. = 2x4 – x³ + 6x³ + 4x² - 3x² - 4x² + 12x + 2x - 8 = 2x4 + 5x³ - 3x² + 14x - 8
Multiplying polynomials :Multiplying polynomials To see this example of multiplication “in your head” again click here. To end this presentation click here.