Multiplying PolynomialsMultiplying Polynomials

How do we find the area of a How do we find the area of a square?square?

The correct formula is written above.The correct formula is written above.

Use it to find the area of the square below.Use it to find the area of the square below.

As2

X

X

As we have already said, to find the area, As we have already said, to find the area, we we

square the length of a side. square the length of a side.

Ax 2X

X

What happens to the area if we What happens to the area if we add 3 units to the length and 1 add 3 units to the length and 1

unit to the width?unit to the width?

---------3--------

1

X

X

This definitely increases the This definitely increases the area. How can we find the area. How can we find the

area of the new shape?area of the new shape?

One way would be to add the One way would be to add the areas of the individual areas of the individual

rectangles that we have rectangles that we have formed.formed.

3x

3

---------3--------

X

X2

1

X

X

x2 x 3x 3

x2 4x 3

Another way of doing this Another way of doing this would be using the formula would be using the formula for the area of a rectangle?for the area of a rectangle?

A=lwA=lw

---------3--------

1

X

X

A=(x+3)(x+1)

How do we get from (x+3)(x+1) How do we get from (x+3)(x+1) to ?to ?

We have already seen that 2(x+1) = 2x+2We have already seen that 2(x+1) = 2x+2

We were able to do this multiplication by We were able to do this multiplication by using the using the

distributive property. We can also use the distributive property. We can also use the

distributive property when we are multiplying distributive property when we are multiplying

polynomials by polynomials.polynomials by polynomials.

x2 4x 3

We need to remember to distribute each We need to remember to distribute each

term in the first set of parentheses through term in the first set of parentheses through

the second set of parentheses.the second set of parentheses.

Example: Example:

(X+3)(x+1)(X+3)(x+1)==(x)(x)+(x)(1)(x)(x)+(x)(1)++(3)(x)+(3)((1)(3)(x)+(3)((1)

x2 x 3x 3

x2 4x 3

Let’s work a few of these.Let’s work a few of these.

1.) (x+2) (x+8)1.) (x+2) (x+8)

2.) (x+5) (x-7)2.) (x+5) (x-7)

3.) (2x+4) (2x-3)3.) (2x+4) (2x-3)

Check your answers.Check your answers.

1.) (x+2) (x+8) = 1.) (x+2) (x+8) = XX22+10x+16+10x+16

2.) (x+5) (x-7) = 2.) (x+5) (x-7) = XX22-2x-35-2x-35

3.) (2x+4) (2x-3) = 3.) (2x+4) (2x-3) = 4x4x22+2x-12+2x-12

By learning to use the distributive property, By learning to use the distributive property, you will be able to multiply any type of you will be able to multiply any type of

polynomialspolynomials..

Example:Example: (x+1)(x(x+1)(x22+2x+3) +2x+3)

(x+1)(x(x+1)(x22+2x+3) +2x+3) = X= X33+2x+2x22+3x+x+3x+x22+2x+3+2x+3

x3 3x2 5x 3