Multiplying Polynomials

Multiplying Polynomials

May 3rd, 2021

Today we are going to learn how to multiply two polynomials.

But first...

Open Ended

Simplify.

 $2\left(x+4\right)$  

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Simplify.

 $-3\left(2-5x\right)$  

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Simplify.

 $6\left(2+3x\right)-10$  

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Simplify.

 $\left(3x\right)\left(-4x\right)$  

Multiplying by a monomial.

Examples:

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Simplify.
 $\left(3x\right)\left(2x^2-4x+3\right)$  

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Simplify.
 $-2x^2\left(6-2x+4x^2\right)$  

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Who is the best? Why?

Binomial * Binomial

Binomial * Binomial

Examples:

Multiple Choice

Using the box method, what is the product of the following binomials?

 $\left(x+4\right)\left(x-5\right)$  

•  $-20+x^2-x$  

•  $x^2-x-20$  

Multiple Choice

Using the distribution method, what is the product of the following binomials?

 $\left(5x+2\right)\left(x-3\right)$  

•  $5x^2-13x-6$  

•  $-6-13x+5x^2$  

Binomial * Trinomial

Binomial * Trinomial

Example:

Binomial * Trinomial

Example:

Multiple Choice

Using the box method, what is the product of the following polynomials?

 $\left(x+4\right)\left(x^2+3x-1\right)$  

•  $x^3+7x^2+11x-4$  

•  $-4+11x+7x+x^3$  

•  $-x^3-7x^2-11x+4$  

Open Ended

Simplify. $\left(6x+1\right)\left(x^2-4x+2\right)$