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

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

Question 8

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

Accepted Answer

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

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

Accepted Answer

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

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

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

Question 18

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

Accepted Answer

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

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

Study Guide - Practice Questions