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Q4.

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Found in: Page 33

Precalculus Mathematics for Calculus

Book edition 7th Edition
Author(s) James Stewart, Lothar Redlin, Saleem Watson
Pages 948 pages
ISBN 9781337067508

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

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

See the 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:

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