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**Multiplying Polynomials**

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

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**The correct formula is written above.**

Use it to find the area of the square below.

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

square the length of a side.

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**What happens to the area if we add 3 units to the length and 1 unit to the width?**

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**This definitely increases the area**

This definitely increases the area. How can we find the area of the new shape?

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**One way would be to add the areas of the individual rectangles that we have formed.**

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

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

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

We have already seen that 2(x+1) = 2x+2 We were able to do this multiplication by using the distributive property. We can also use the distributive property when we are multiplying polynomials by polynomials.

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**We need to remember to distribute each**

term in the first set of parentheses through the second set of parentheses. Example: (X+3)(x+1)=(x)(x)+(x)(1)+(3)(x)+(3)((1)

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**Let’s work a few of these.**

1.) (x+2) (x+8) 2.) (x+5) (x-7) 3.) (2x+4) (2x-3)

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**Check your answers. 1.) (x+2) (x+8) = X2+10x+16**

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**(x+1)(x2+2x+3) = X3+2x2+3x+x2+2x+3**

By learning to use the distributive property, you will be able to multiply any type of polynomials. Example: (x+1)(x2+2x+3) (x+1)(x2+2x+3) = X3+2x2+3x+x2+2x+3

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