Q4. - Algebra 1

Question

Write an expression for the area of the rectangle below.

$$\begin{gathered} \mathrm{F}\mathbf{10}{b}^5{c}^5-\mathbf{3}bc \\ \mathrm{G}\mathbf{10}{b}^5{c}^5-\mathbf{15}{b}^2{c}^3 \\ \mathrm{H}\mathbf{2}{b}^5{c}^5-\mathbf{3}{b}^2{c}^3 \\ \mathrm{J}\mathbf{10}{b}^4{c}^6-\mathbf{15}b{c}^2 \end{gathered}$$

Step-by-Step Solution

Answer

The area of the rectangle is $\mathbf{10}{b}^5{c}^5-\mathbf{15}{b}^2{c}^3$.

Step 1. Write the formula of the area of a rectangle.

Area of rectangle is given by $A=\text{length}\times \text{width}$.

Step 2. Substitute.

Substitute $2b^4{c}^3-3bc$ for length and $5b{c}^2$ into $A=\text{length}\times \text{width}$.

 

 $A=\left(2b^4{c}^3-3bc\right)5b{c}^2$

Step 3. Simplify.

Simplify the above-obtained expression.

 

$$\begin{gathered} A=\left(2b^4{c}^3-3bc\right)5b{c}^2 \\ =2b^4{c}^3\cdot 5b{c}^2-3bc\cdot 5b{c}^2 \\ =10b^5{c}^5-15b^2{c}^3 \end{gathered}$$ 

 

Therefore, the area of the rectangle $10b^5{c}^5-15b^2{c}^3$ completely matches option G. Option G is the required answer.