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Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset Vaia Explanations$ Math

Student Edition · 801 pages

ISBN: 9780078884801

Chapter 7: Q46. (page 462)

Find the area of the rectangle.

Short Answer

Expert verified

The area of the rectangle is $(3 x^{3} + 3 x^{2} - 21 x)$ units².

Step by step solution

01

Step 1. Define an expression.

A mathematical expression is a combinations of numbers and variables ordered with mathematical operations.

02

Step 2. Define the power of a product rule.

Power of a product rule states that if the two exponents of the same base are multiplied then the exponents are added and base remains the same.

$a^{m} . a^{n} = a^{m + n}$

Where, $a$ is any non-zero real number.

03

Step 3. Define the area of the rectangle.

Area of the rectangle $(A)$ lengthwidth ……….. (1)

04

Step 4. Calculate the area of the given rectangle.

Observe the figure.

Let the length of the rectangle $= x^{2} + x - 7$ units

The width of the rectangle $= 3 x$ units

Use the equation (1).

The area of the rectangle is

$\begin{array}{l} A = (x^{2} + x - 7) (3 x) \\ A = x^{2} (3 x) + x (3 x) - 7 (3 x) \end{array}$

Use the power of a product rule.

$A = 3 x^{3} + 3 x^{2} - 21 x$

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Most popular questions from this chapter

Express each number in standard form.

$2.9 \times 10^{- 5}$

Determine whether the given expression is a monomial. Write yes or no.

Explain your reasoning.

$\frac{r}{2}$

GEOMETRY Use the formula $V = π r^{2} h$ to find the volume of the cylinder.

Find each product.

$(x - 3) (x^{2} + 5 x - 6)$

Determine whether the given expression is a monomial. Write yes or no.

Explain your reasoning.

$3 a^{4}$

See all solutions

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