Q46. - Algebra 1

Question

Find the area of the rectangle.

Step-by-Step Solution

Answer

The area of the rectangle is $\left(3x^3+3x^2-21x\right)$ units².

Step 1. Define an expression.

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

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.

Step 3. Define the area of the rectangle.

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

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 $=3x$ units

Use the equation (1).

The area of the rectangle is

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

Use the power of a product rule.

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