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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. 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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Lets 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) = X 2 +10x+16 2.) (x+5) (x-7) = X 2 -2x-35 3.) (2x+4) (2x-3) = 4x 2 +2x-12

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

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