Multiplying Polynomials

MATH 017

Intermediate Algebra

S. Rook

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Overview

• Section 5.4 in the textbook– Multiply by monomials– Multiply binomials– Square binomials– Multiply (a + b)(a – b)– Multiply more than two polynomials

Multiplying by a Monomial

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Multiplying by a Monomial

• Use the distributive property

• Simplify using exponent rules

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Multiplying by a Monomial (Example)

Ex 1: Multiply: xxx 29 32

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Multiplying by a Monomial (Example)

Ex 2: Multiply: 7442 2634 xyxyyx

Multiply Binomials

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Multiplying Polynomials in General

• To multiply (4x + 3)(2x2 – 3x + 7), we use the distributive property= 4x(2x2 – 3x + 7) + 3(2x2 – 3x + 7)

• Simplify and combine any like terms

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Multiplying Polynomials in General (Example)

Ex 3: Multiply (3x2 + 4x – 5)(3x + 2)

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Multiplying Binomials

• Recall that a binomial is a polynomial with 2 terms

• Can also use the distributive property• A helpful pneumonic is FOIL (essentially

the distributive property)F irstO uterI nnerL ast

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Multiplying Binomials (Example)

Ex 4: Multiply: (4x + 5)(3x - 2)

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Multiplying Binomials (Example)

Ex 5: Multiply: (2x - 7)(x - 8)

Square Binomials

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Square Binomials

• First expand: (a + b)2 = (a + b)(a + b)

• Finally use FOIL

• Do NOT just square each of the individual terms!

(a + b)2 ≠ a2 + b2

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Square Binomials (Example)

Ex 6: Multiply: (3x + 2y)2

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Square Binomials (Example)

Ex 7: Multiply: (4x – 5)2

Multiply (a + b)(a – b)

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Multiply (a + b)(a – b)

• A special product

• Use FOIL to simplify

• The O and the I terms cancel

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Multiply (a + b)(a – b) (Example)

Ex 8: Multiply (m – 3n)(m + 3n)

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Multiply (a + b)(a – b) (Example)

Ex 9: Multiply (2r4 + 5s2)(2r4 – 5s2)

Multiply More than Two Polynomials

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Multiply More than Two Polynomials

• Multiply the first two polynomials using the techniques discussed thus far

• Use the distributive property to multiply the result by the last polynomial

• Simplify

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Multiply More than Two Polynomials (Example)

Ex 10: Multiply (x + 2)(x – 7)(x + 1)

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Multiply More than Two Polynomials (Example)

Ex 11: Multiply (x + 4)2(7x – 2)

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Summary

• After studying these slides, you should know how to do the following:– Multiply by monomials– Multiply binomials– Square binomials– Multiply (a + b)(a – b)– Multiply more than two polynomials