Q. 275 - Intermediate Algebra

Question

In the following exercises , simplify the equation ${\left(3d\hspace{0.17em}+\hspace{0.17em}1\right)}^2$.

Step-by-Step Solution

Answer

The simplified expression is $9d^2+6d+1$.

Step 1. Given Information.

The expression is ${\left(3d\hspace{0.17em}+\hspace{0.17em}1\right)}^2$.

Step 2. Simplify given equation.

Simplifying ${\left(3d\hspace{0.17em}+\hspace{0.17em}1\right)}^2$

Apply perfect square formula:-

$$\begin{gathered} {\left(a+b\right)}^2=a^2+2ab+b^2 \\ {\left(3d+1\right)}^2={\left(3d\right)}^2+2·\hspace{0.17em}3d·\hspace{0.17em}1+1^2 \\ {\left(3d\right)}^2+2·\hspace{0.17em}3d·\hspace{0.17em}1+1^2=9d^2+6d+1 \end{gathered}$$