Section 4.5Multiplication of Polynomials

Use the Distributive Property when indicated.

Remember: when multiplying 2 powers that have like bases, we ADD their exponents!

Multiplying by a Monomial

1) (-2x6)(8x8)

2) 7a2bc4(-2a5b7c)

3) -2x(2x2 – 3x – 5)

4) (5x2 – 3xy + 5)(3x)

Ex: Multiply

FOIL is an acronym that represents the distributive property. ONLY works for 2 binomials!

F – multiply the first terms of each binomialO – multiply the outer termsI – multiply the inner termsL – multiply the last terms of each binomial

Then… combine any like terms to finish!

Multiplying 2 Binomials: FOIL

1) (x + 2)(x + 4) 2) (x – 6)(x + 2) 3) (3x – 4)(x + 2) 4) (4 – 2x)(6 – 5x) 5) (2x + 3)(2x – 3) 6) (4x + 1)2

EX: multiply using FOIL

1. The SUM and DIFFERNENCE Product◦(a + b)(a – b) = a2 – b2

2. The Square of a BINOMIAL◦(a + b)2 = a2 + 2ab + b2

◦(a - b)2 = a2 - 2ab + b2

Formulas for Special Products

1) (3X + 4)(3X – 4) 2) (9X – 1)(9X + 1)

3) (X – 6)2

4) (2X + 3)2

Ex: multiply using the formulas

Expand the distributive property so that every term in the 1st polynomial gets multiplied to every term in the 2nd polynomial.

Then, just combine like terms!

Multiplying any 2 Polynomials

1) (x2 – 4x + 3)(3x2 – 4)

2) (4a3 +2a2 – a + 4)(2a2 + 2a)3

3) (3x + 2)(4x2 + x – 3)

Ex: multiply