### About Special Polynomial Products:

When we multiply polynomials, we find that some problems occur very often. For these types of problems, generally called special products, we can develop shortcut formulas. When memorized, these formulas allow us to multiply these special products very quickly.

Test Objectives

- Demonstrate a general understanding of special products formulas
- Demonstrate the ability to quickly square a binomial
- Demonstrate the ability to quickly cube a binomial

#1:

Instructions: Find each product.

a) (8a - 5)^{2}

b) (2 + 3n)^{2}

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#2:

Instructions: Find each product.

a) $$\left(\frac{3n}{5}+ \frac{1}{4}\right)^2$$

b) $$\left(\frac{7x}{4}- \frac{5}{4}\right)^2$$

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#3:

Instructions: Find each product.

a) (6 + 4v)(6 - 4v)

b) (4x - 2)(4x + 2)

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#4:

Instructions: Find each product.

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

b) (-7u + 9v)(-7u - 9v)

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#5:

Instructions: Find each product.

a) (8b - 3)^{3}

b) $$\left(\frac{z^2}{4}+ \frac{2y}{5}\right)^3$$

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Written Solutions:

#1:

Solutions:

a) 64a^{2} - 80a + 25

b) 9n^{2} + 12n + 4

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#2:

Solutions:

a)

9n^{2} | + | 3n | + | 1 |

25 | 10 | 16 |

b)

49x^{2} | - | 35x | + | 25 |

16 | 8 | 16 |

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#3:

Solutions:

a) -16v^{2} + 36

b) 16x^{2} - 4

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#4:

Solutions:

a) 4x^{6} - 9y^{4}

b) 49u^{2} - 81v^{2}

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#5:

Solutions:

a) 512b^{3} - 576b^{2} + 216b - 27

b)

z^{6} | + | 3z^{4}y | + | 3z^{2}y^{2} | + | 8y^{3} |

64 | 40 | 25 | 125 |