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Chapter 4

Polynomials

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Multiplication of Polynomials

• Multiplying Monomials

• Multiplying a Monomial and a Polynomial

• Multiplying Any Two Polynomials

4.5

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To Multiply Monomials

To find an equivalent expression for the product of two monomials, multiply the coefficients and then multiply the variables using the product rule for exponents.

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Example

Multiply: a) (6x)(7x) b) (5a)(a) c) (8x6)(3x4)

Solution

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Example

Multiply: a) x and x + 7 b) 6x(x2 4x + 5)

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The Product of a Monomial and a Polynomial

To multiply a monomial and a polynomial, multiply each term of the polynomial by the monomial.

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Example

Multiply: 5x2(x3 4x2 + 3x 5)

Solution

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Example

Multiply each of the following.a) x + 3 and x + 5 b) 3x 2 and x 1Solution

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The Product of Two Polynomials

To multiply two polynomials P and Q, select one of the polynomials, say P. Then multiply each term of P by every term of Q and combine like terms.

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Example

Multiply: (5x3 + x2 + 4x)(x2 + 3x)

Solution

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Example

Multiply: (3x2 4)(2x2 3x + 1)

Solution