Q. 276 - Intermediate Algebra

Question

In the following exercises , simplify the equation ${\left(4a\hspace{0.17em}+\hspace{0.17em}10\right)}^2$.

Step-by-Step Solution

Answer

The simplified expression is $16a^2+80a+100$.

Step 1. Given Information.

The expression is ${\left(4a\hspace{0.17em}+\hspace{0.17em}10\right)}^2$.

Step 2. Simplify given equation.

Simplifying ${\left(4a\hspace{0.17em}+\hspace{0.17em}10\right)}^2$

Apply perfect square formula:-

$$\begin{gathered} {\left(a+b\right)}^2=a^2+2ab+b^2 \\ {\left(4a+10\right)}^2={\left(4a\right)}^2+2·\hspace{0.17em}4a·\hspace{0.17em}10+{10}^2 \\ {\left(4a\right)}^2+2·\hspace{0.17em}4a·\hspace{0.17em}10+{10}^2 = 16a^2+80a+100 \end{gathered}$$