Question

The Special Product Formula for the “square of a sum” is${\left(A+B\right)}^2=$_______ . So,${\left(2x+3\right)}^2=$_______

Short answer

The Special Product Formula for the “square of a sum” is ${\left(A+B\right)}^2=A^2+2AB+B^2$. So,${\left(2x+3\right)}^2=4x^2+12x+9$

Step-by-step solution

Step 1. Apply the square of a sum formula.

If A and B are any real numbers or algebraic expressions, then

${\left(A+B\right)}^2=A^2+2AB+B^2$

Step 2. Analyze the given expression.

Given${\left(2x+3\right)}^2$

Here$A=2x,B=3$

Step 3. Find the square of the sum.

Substitute the values in the square of the sum formula to get:

$\begin{array}{l}{\left(2x+3\right)}^2={\left(2x\right)}^2+2\cdot 2x\cdot 3+3^2\\ \Rightarrow {\left(2x+3\right)}^2=4x^2+12x+9\end{array}$