### About Special Products:

When we multiply with polynomials, some problem types repeat themselves often. We generally refer to these as special products. It is very beneficial to memorize the formulas for all of the special products. This will allow us to conduct the multiplication in such a scenario very quickly.

Test Objectives

- Demonstrate the ability to quickly find the product of a binomial squared
- Demonstrate the ability to quickly find the product of the sum and difference of the same two terms
- Demonstrate the ability to quickly find the product of a binomial cubed

#1:

Instructions: Find each product.

a) (x + 4)^{2}

b) (4x - 8)(4x + 8)

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#2:

Instructions: Find each product.

a) (2u - 7v)(2u + 7v)

b) (5x^{2} + 7y^{2})(5x^{2} - 7y^{2})

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#3:

Instructions: Find each product.

a) (6 + 4p^{2})^{2}

b) (10y^{2} + 8x)^{2}

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#4:

Instructions: Find each product.

a) (7n^{3} - 10m)^{2}

b) (-10x^{2} - 10y^{2})^{2}

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#5:

Instructions: Find each product.

a) (5x^{2} + 3y^{3})^{3}

b) (9x^{3}z^{5} - 2y^{4})^{3}

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Written Solutions:

#1:

Solutions:

a) x^{2} + 8x + 16

b) 16x^{2} - 64

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#2:

Solutions:

a) 4u^{2} - 49v^{2}

b) 25x^{4} - 49y^{4}

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#3:

Solutions:

a) 16p^{4} + 48p^{2} + 36

b) 100y^{4} + 160xy^{2} + 64x^{2}

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#4:

Solutions:

a) 49n^{6} - 140n^{3}m + 100m^{2}

b) 100x^{4} + 200x^{2}y^{2} + 100y^{4}

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#5:

Solutions:

a) 125x^{6} + 225x^{4}y^{3} + 135x^{2}y^{6} + 27y^{9}

b) 729x^{9}z^{15} - 486x^{6}y^{4}z^{10} + 108x^{3}y^{8}z^{5} - 8y^{12}