Question

select the correct answer.
simplify the following expression.
$(4x + 7)^2$
a. $16x^2 - 49$
b. $16x^2 + 56x + 49$
c. $16x^2 + 28x + 49$
d. $16x^2 + 49$

Explanation:

Step1: Recall square of sum formula

The formula for squaring a binomial is $(a+b)^2 = a^2 + 2ab + b^2$, where $a=4x$ and $b=7$.

Step2: Calculate $a^2$

$a^2 = (4x)^2 = 16x^2$

Step3: Calculate $2ab$

$2ab = 2\times4x\times7 = 56x$

Step4: Calculate $b^2$

$b^2 = 7^2 = 49$

Step5: Combine the terms

Add the results from Steps 2-4: $16x^2 + 56x + 49$

Answer:

B. $16x^2 + 56x + 49$