February 14th February 14th ## Special ProductsAfter studying this lesson, you will be able to: - Use Special Products Rules to multiply certain polynomials.
We will consider three special products in this section.
## Square of a Sum(a + b)
(x + 3) We are squaring a sum. We can just write the binomial down twice and multiply using the FOIL Method or we can use the Square of a Sum Rule. Using the Square of a Sum Rule, we: square the first term which is x...this will give us x multiply the 2 terms together and double them x times 3 is 3x... double it to get 6x square the last term which is 3...this will give us 9 The answer is x
(x + 2) We are squaring a sum. We can just write the binomial down twice and multiply using the FOIL Method or we can use the Square of a Sum Rule. Using the Square of a Sum Rule, we: square the first term which is x...this will give us x multiply the 2 terms together and double them x times 2 is 2x... double it to get 4x square the last term which is 2...this will give us 4 The answer is x
## Square of a Difference(a - b)
(x - 2) We are squaring a difference. We can just write the binomial down twice and multiply using the FOIL Method or we can use the Square of a Sum Rule. Using the Square of a Difference Rule, we: square the first term which is x...this will give us x multiply the 2 terms together and double them x times -2 is 2x...double it to get -4x square the last term which is -2...this will give us 4 The answer is x
## Product of a Sum and a Difference(a + b)(a - b) = a
( x + 5 ) ( x - 5 ) We have the product of a sum and a difference. Here's what we do: multiply the first terms x times x will be x multiply the last terms 5 times 5 will be -25 The answer is x
( x + 7 ) ( x - 7 ) We have the product of a sum and a difference. Here's what we do: multiply the first terms x times x will be x multiply the last terms 7 times 7 will be - 49 The answer is x |

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