1 3x 24x 3 Multiply the firsts 3x 2 4x 3 3x 4x 12x 2 Multiply the outsides 3x

1 3x 24x 3 multiply the firsts 3x 2 4x 3 3x 4x 12x 2

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1) (3x 2)(4x + 3) Multiply the “ firsts ( 3x 2)( 4x + 3) 3x 4x = 12x 2 Multiply the “ outsides ( 3x 2)(4x + 3 ) 3x 3 = 9x Multiply the “ insides (3x 2 )( 4x + 3) 2 4x = 8x Multiply the “ lasts (3x 2 )(4x + 3 ) 2 3 = 6 F O I L Now combine like terms 12x 2 + 9x 8x 6 = 12x 2 + x 6 2) (y + 2)(y + 5) Firsts ( y + 2)( y + 5) y y = y 2 Outsides ( y + 2)(y + 5 ) y 5 = 5y Insides (y + 2 )( y + 5) 2 y = 2y Lasts (y + 2 )(y + 5 ) 2 5 = 10 F O I L Now combine like terms y 2 + 5y + 2y + 10 = y 2 + 7y + 10
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3) (a 8)(a 9) F O I L a 2 9a 8a + 72 = a 2 17a + 72 4) (3b + 2)(3b 5) F O I L 9b 2 15b + 6b 10 = 9b 2 9b 10 5) (4y 5)(2y 3) F O I L 8y 2 12y 10y + 15 = 8y 2 22y + 15
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Multiplying Two Binomials with Special Products There are two special cases of FOIL multiplication that are worth noting: The product of the sum and difference of two binomials (a + b)(a b) = a 2 + ab ab b 2 = a 2 b 2 The square of a binomial (a + b) 2 = (a + b)(a + b) = a 2 + ab + ab + b 2 = a 2 + 2ab + b 2 (a b) 2 = (a b)(a b) = a 2 ab ab + b 2 = a 2 2ab + b 2 Study these examples: 1) (2x + 3)(2x 3) = 4x 2 6x + 6x 9 FOIL = 4x 2 9 Combine like terms. 2) (y + 3)(y 3) = y 2 3y + 3y 9 FOIL = y 2 9 Combine like terms. 3) (x 2y)(x + 2y) = x 2 4y 2 (a +b)(a b) = a 2 b 2 4) (2a + 5c)(2a 5c) = 4a 2 25c 2 (a +b)(a b) = a 2 b 2 5) (x + 5) 2 = (x + 5)(x + 5) = x 2 + 5x + 5x + 25 FOIL = x 2 + 10x + 25 Combine like terms. 6) (2x 3) 2 = (2x 3)(2x 3) = 4x 2 12x + 9 (a b) 2 = a 2 2ab + b 2 7) (3x + 2y) 2 = (3x + 2y)(3x + 2y) = 9x 2 + 12xy + 4y 2 (a + b) 2 = a 2 + 2ab + b 2
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Dividing Monomials Use the rules of exponents and experience with fractions to aid in dividing monomials. Let us look at an example: 8x 6 ÷ 4x 2 6 6 2 2 8x 8 x 4x 4 x Rewrite as a fraction. 6 6 2 2 8 x x 2 4 x x Simplify the constants. 6 2 4 6 2 x 2 2x x 2x Apply the rule of exponents x a /x b = x a b
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