**9.**

(2 *x*^{2}^{x}

7) ( 3 *x*^{2}^{6} *x*

2)

**10.**

(3 *x*^{2}^{5} *x*

2) (2 *x*^{2}^{4} *x*

9)

**11.**

( 7 *x*^{2}_{5} *x*

8) ( 4 *x* 9 *x*^{2}

10)

**12.**

(8 *x*^{3}_{7} *x*^{2}

10) (7 *x*^{3}_{8} *x*^{2}_{9} *x* )

**13.**

(2 *x*^{4}^{7} *x*^{2}

8) (3 *x*^{2}^{2} *x*^{4}

9)

**14.**

(4 *x*^{2}^{9} *x*

2) (5 3 *x* 5 *x*^{2}^{)}

**15.**

(7 *z*^{2}

2) (5 *z*^{2}_{2} *z*

1)

**16.**

(25 *y*^{3}_{7} *y*^{2}_{9} *y* ) (14 *y*^{2}_{7} *y*

2)

**17.**

(3 *y*^{3}_{7} *y*^{2}_{8} *y*

4) (14 *y*^{3}_{8} *y* 9 *y*^{2}_{)}

**18.**

(2 *x*^{2}_{3} *xy* ) ( *x*^{2}_{8} *xy* 7 *y*^{2}_{)}

**19.**

(6 *x* 2 *y* ) 2(5 *x* 7 *y* )

**20.**

3 *a* [2 *a*^{2}^{(5} *a* 4 *a*^{2}

3)]

**21.**

(2 *x*^{2}

2) ( *x*

1) ( *x*^{2}

5)

**22.**

(3 *x*^{3}

1) (3 *x*^{2}

1) (5 *x*

3)

**23.**

(4 *t* *t*^{2}^{t}^{3}^{)} (3 *t*^{2}^{2} *t* 2 *t*^{3}^{)} (3 *t*^{3}

1)

**24.**

( *z*^{3}^{2} *z*^{2}^{)} ( *z*^{2}^{7} *z*

1) (4 *z*^{3}^{3} *z*^{2}^{3} *z*

2)

**In Exercises 25–64, multiply the polynomials and write the expressions in standard form.**

**25.**

5 *xy*^{2}_{(7} *xy* )

**26.**

6 *z* (4 *z*^{3}_{)}

**27.**

2 *x*^{3}_{(1} *x* *x*^{2}_{)}

**28.**

4 *z*^{2}_{(2} *z* *z*^{2}_{)}

**29.**

2 *x*^{2}^{(5} *x* 5 *x*^{2}^{)}

**30.**

**31.**

( *x*^{2}^{x}

2)2 *x*^{3}

**32.**

( *x*^{2}^{x}

2)3 *x*^{3}

**33.**

2 *ab*^{2}_{(} *a*^{2}_{2} *ab* 3 *b*^{2}_{)}

**34.**

*bc ^{3}_{d}^{2}_{(} b^{2}_{c} cd^{3}_{b}^{2}_{d}^{4}_{)}*

**35.**

(2 *x*

1)(3 *x*

4)

**36.**

(3 *z*

1)(4 *z*

7)

**37.**

( *x*

2)( *x*

2)

**38.**

( *y*

5)( *y*

5)

**39.**

(2 *x*

3)(2 *x*

3)

**40.**

(5 *y*

1)(5 *y*

1)

**41.**

(2 *x*

1)(1 2 *x* )

**42.**

(4 *b* 5 *y* )(4 *b* 5 *y* )

**43.**

(2 *x*^{2}

3)(2 *x*^{2}

3)

**44.**

(4 *xy*

9)(4 *xy*

9)

**45.**

(7 *y* 2 *y*^{2}^{)(} *y* *y*^{2}

1)

**46.**

(4 *t*^{2}^{)(6} *t* 1 *t*^{2}^{)}

**47.**

( *x*

1)( *x*^{2}^{2} *x*

3)

**48.**

( *x*

3)( *x*^{2}^{3} *x*

9)

-^{1}

2^{z} (2 *z* + 4 *z*^{2}^{-}

10)

EXERCISES

**SECTION**

0.3

**Perfect Squares**

Square of a binomial sum.

( *a* *b* )^{2}_{(} *a* *b* )( *a* *b* ) *a*^{2}_{2} *ab* *b*^{2}

Square of a binomial difference.

( *a* *b* )^{2}_{(} *a* *b* )( *a* *b* ) *a*^{2}_{2} *ab* *b*^{2}

**Perfect Cubes**

Cube of a binomial sum.

( *a* *b* )^{3}^{a}^{3}^{3} *a*^{2}^{b} 3 *ab*^{2}^{b}^{3}

Cube of a binomial difference.

( *a* *b* )^{3}^{a}^{3}^{3} *a*^{2}^{b} 3 *ab*^{2}^{b}^{3}

In this section, polynomials were defined. Polynomials with one, two, and three terms are called monomials, binomials, and trinomials, respectively. Polynomials are added and subtracted by combining like terms. Polynomials are multiplied by distributing the monomials in the first polynomial throughout the second polynomial. In the special case of the product of two binomials, the FOIL method can also be used. The following are special products of binomials.

**Difference of Two Squares**

( *a* *b* )( *a* *b* ) *a*^{2}_{b}^{2}

SUMMARY

**SECTION**

0.3

■^{SKILLS}

36_{CHAPTER 0} Prerequisites and Review

**65. Profit.**

Donna decides to sell fabric cord covers on eBay for $20 a piece. The material for each cord cover costs $9, and it costs her $100 a month to advertise on eBay. Let *x* be the number of cord covers sold. Write a polynomial representing her monthly profit.

**66. Profit.**

Calculators are sold for $25 each. Advertising costs are $75 per month. Let *x* be the number of calculators sold. Write a polynomial representing the monthly profit earned by selling *x* calculators.

**67. Profit.**

If the revenue associated with selling *x* units of a product is *R* *x*^{2}^{100} *x* , and the cost associated with producing *x* units of the product is *C* 100 *x* 7500, find the polynomial that represents the profit of making and selling *x* units.

**68. Profit.**

A business sells a certain quantity *x* of items. The revenue generated by selling *x* items is given by the equation . The costs are given by *C* 8000 150 *x* . Find a polynomial representing the net profit of this business when *x* items are sold.

**69. Volume of a Box.**

A rectangular sheet of cardboard is to be used in the construction of a box by cutting out squares of side length *x* from each corner and turning up the sides.

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- Summer '17
- juan alberto
- Algebra, Distributive Property, GCF