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4.5 Multiplying Polynomials

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4.5 Multiplying Polynomials

Multiply a monomial and a polynomial.

Slide 4.5-3

To find the product of a monomial and a polynomial with more than one term we use the distributive property and multiplication of monomials.

Do not confuse addition of terms with multiplication of terms. For instance,

but

As shown in Section 4.1, we find the product of two monomials by using the rules for exponents and the commutative and associative properties. For example

Slide 4.5-4

Find the product.

CLASSROOM EXAMPLE 1

Multiplying Monomials and Polynomials

Solution:

Slide 4.5-5

Multiply two polynomials.

Slide 4.5-6

We can use the distributive property repeatedly to find the product of any two polynomials. For example, to find the product of the polynomials x2 + 3x +5 and x − 4, think of x − 4 as a single quantity and use the distributive property as follows.

Now use the distributive property three more times to find x2(x − 4), 3x(x − 4), and 5(x − 4).

Multiplying Polynomials

To multiply two polynomials, multiply each term of the second polynomial by each term of the first polynomial and add the products.

Slide 4.5-7

Multiply (m3 −2m + 1)·(2m2 + 4m + 3).

CLASSROOM EXAMPLE 2

Multiplying Two Polynomials

Solution:

Slide 4.5-8

Multiply.

CLASSROOM EXAMPLE 3

Multiplying Polynomials Vertically

Solution:

Slide 4.5-9

Find the product of

CLASSROOM EXAMPLE 4

Multiplying Polynomials with Fractional Coefficients Vertically

Solution:

Slide 4.5-10

Multiply binomials by the FOIL method.

Slide 4.5-11

Multiplying Binomials by the FOIL Method

Step 1:Multiply the twoFirstterms of the binomials to get the first term of the answer.

In algebra, many times the polynomials to be multiplied are binomials. For these products, the FOIL methodreduces the rectangle method to a systematic approach without the rectangle.

Step 2:Find theOuter product andInner product and add them (when possible) to get the middle term of the answer.

Step 3:Multiply the twoLast terms of the binomials to get the last term of the answer.

Slide 4.5-12

Use the FOIL method to find the product.

CLASSROOM EXAMPLE 5

Using the FOIL Method

Solution:

Slide 4.5-13

Multiply

CLASSROOM EXAMPLE 6

Using the FOIL Method

Solution:

Slide 4.5-14

Find each product.

CLASSROOM EXAMPLE 7

Using the FOIL Method

Solution:

Slide 4.5-15