 # Multiplying Binomials Objectives: To Multiply Two Binomials FOIL To multiply the sum and difference of two expressions To square a binomial.

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Multiplying Binomials Objectives: To Multiply Two Binomials FOIL To multiply the sum and difference of two expressions To square a binomial

Example 1 Multiply. (x + 2)(x + 3) = (x)(x) + = x 2 + = x 2 + 5x + 6 (x)(3) +(2)(x) +(2)(3) 3x +2x+ 6 FOIL irstirst utsideutside insideinside astast

Example 2 Multiply. (3x + 2)(x + 5) = (3x)(x) + = 3x 2 + 15x + 2x + 10 = 3x 2 + 17x + 10 (3x)(5) +(2)(x) +(2)(5)

Example 3 Multiply. (4ab + 3)(2a 2 b + 1) = (4ab)(2a 2 b) + = 8a 3 b 2 + (4ab)(1) +(3)(2a 2 b) +(3)(1) 4ab +6a 2 b +3

Practice 1 1) (x + 3)(x + 4) Multiply. 2) (x + 3)(x – 5) 3) (2x + 1)(x + 4)

Practice 2 Multiply. 4) (2x 2 – 3)(x – 2) 5) (6x 2 + 5)(2x 3 + 1) 6) (2xy + 4x)(-2y + y 2 )

Multiplying Binomials – Special Products Objectives: To multiply the sum and difference of two expressions To square a binomial

Example 1 Multiply. (x + 6)(x – 6) = (x)(x) + (x)(-6) + (6)(x) + (6)(-6) = x 2 – 6x + 6x - 36 = x 2 - 36

Example 2 Multiply. (2x + 4)(2x – 4) = (2x)(2x) + (2x)(-4) + (4)(2x) + (4)(-4) = 4x 2 – 8x + 8x - 16 = 4x 2 - 16

Example 3 Multiply. (-3x + 4y)(-3x – 4y) = (-3x)(-3x) + (-3x)(-4y) + (4y)(-3x) + (4y)(-4y) = 9x 2 + 12xy – 12xy – 16y 2 = 9x 2 – 16y 2

Practice 1) (x + 2)(x – 2) Multiply. 2) (x 2 + 7)(x 2 – 7) 3) (3x + 5)(3x – 5)

Example 4 Multiply. (x + 2) 2 = (x)(x) + (x)(2) + (2)(x) + (2)(2) = x 2 + 2x + 2x + 4 = x 2 + 4x + 4 = (x + 2)(x + 2)

Example 5 Multiply. (x - 3) 2 = (x)(x) + (x)(-3) + (-3)(x) + (-3)(-3) = x 2 - 3x - 3x + 9 = x 2 - 6x + 9 = (x - 3)(x - 3)

Example 6 Multiply. (2x – 3y) 2 = (2x)(2x) + (2x)(-3y) + (-3y)(2x) + (-3y)(-3y) = 4x 2 - 6xy - 6xy + 9y 2 = 4x 2 - 12xy + 9y 2 = (2x – 3y)(2x – 3y)

Practice 1) (x + 3) 2 Multiply. 2) (2x + 1) 2 3) (2y + 4x) 2

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