Question 1

Which of the following is the correct application of the product rule for exponents when multiplying $$5m^3 by$$ $$3m^2$$?

Accepted Answer

$$15m^5$$

Question 2

Simplify the expression $$-6p(p^4 - 8$$)$$ and write your answer in standard form.

Accepted Answer

$$-6p^5 + 48p$

Question 3

A rectangular garden has a length of $$x + 4$$ meters and a width of $$x$$ meters. Write an expression for the area and simplify.

Accepted Answer

$$x^2 + 4x$

Question 4

Distribute and simplify: $$3c^5(-2c - 5$$)$$.

Accepted Answer

$$-6c^6$$ - $$15c^5$$

Question 5

Which of the following expressions represents the area of a trapezoid with bases $$2x^3 - x$ and 8x^2$ + 3x$$, and height $$4x^2$$?

Accepted Answer

$$\frac{1}{2} \cdot 4x^2$ \left[(2x^3$ - x) + (8x^2$ + 3x)\right]$$

Question 6

Simplify $$-2x(3x - 4) + 7x$$ and write your answer in standard form.

Accepted Answer

$$-6x^2 + 15x$

Question 7

A company produces $$p^2q^3$(p^5q^2$ - pq)$ units of a product. Simplify the expression for the total units produced.

Accepted Answer

$$p^7q^5$ - p^3$q^4$$

Question 8

Distribute and simplify: $$5r^2s^2$(-2r^2 + 3rs$$ - $$4s^2$$)$$.

Accepted Answer

$$-10r^4s^2$ + 15r^3$s^3$$ - $$20r^2s^4$

Question 9

A rectangular field has a length of $$3x + 2$$ and a width of $$4x. $$Write an expression for the area and simplify.

Accepted Answer

$$12x^2 + 8x$

Question 10

Simplify $$2y(6x - 4x^2$y) + 13x^2$y^2 - 6$ and write your answer in standard form.

Accepted Answer

$$12xy - 8x^2$y^2$$ + $$13x^2y^2$ - 6$$

Question 11

Which of the following is the correct simplification of $$-3n(n^2 - 2n + 8$$)$$?

Accepted Answer

$$-3n^3$$ + $$6n^2 - 24n$

Question 12

A company’s profit is modeled by $$4b[2a^2$ - 5(3ab - 2b^2$)] + 29ab^2$. Simplify the expression for profit.

Accepted Answer

$$8a^2b$$ - $$60ab^2$$ + $$40b^3$$ + $$29ab^2$$

Question 13

Simplify $$x(x^2 - x + 3$$)$$ and write your answer in standard form.

Accepted Answer

$$x^3$$ - $$x^2 + 3x$

Question 14

A chemical reaction produces $$-2x^4(6x^2$ - 12x + 18)$ grams of a substance. Simplify the expression for the total grams produced.

Accepted Answer

$$-12x^6$$ + $$24x^5$$ - $$36x^4$$

Question 15

Distribute and simplify: $$3ab(4a^2$$ - $$7b^3$$)$$.

Accepted Answer

$$12a^3b$$ - $$21ab^4$$

Question 16

A shaded region in a diagram is represented by the area $$3x + 2$$ times $$4x$$ minus $$2x$$ times $$3x. $$Write the simplified expression for the area.

Accepted Answer

$$6x^2 + 8x$

Question 17

Simplify $$-7c^3d^2$(9c^2d^2$ - 4cd^5$)$ and write your answer in standard form.

Accepted Answer

$$-63c^5d^4$ + 28c^4$d^7$$

Question 18

Which of the following is the correct simplification of $$10m^4n(-2mn^3$ + 3n)$?

Accepted Answer

$$-20m^5n^4$ + 30m^4$n^2$$

Question 19

A business’s cost function is $$2y^2(y^5$ - 4y)$. Simplify the expression for the cost.

Accepted Answer

$$2y^7$$ - $$8y^3$$

Multiplying Monomials and Polynomials: Step-by-Step College Algebra Guidance

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