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Find the square. Simplify your answer. $\newline$ $(4p + 2)^2$

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Multiply two binomials: special cases

Full solution

Q. Find the square. Simplify your answer.

\newline

(4p + 2)^2

Square Binomial Formula: We need to square the binomial $(4p + 2)$ . This is in the form of $(a + b)^2$ , which can be expanded using the formula $(a + b)^2 = a^2 + 2ab + b^2$ .
Identify $a$ and $b$ : Identify the values of $a$ and $b$ in the binomial $(4p + 2)$ . Here, $a = 4p$ and $b = 2$ .
Apply Formula to Expand: Apply the square of a binomial formula to expand $(4p + 2)^2$ . $(4p + 2)^2 = (4p)^2 + 2(4p)(2) + 2^2$
Simplify Each Term: Simplify each term in the expansion. $\newline$ $(4p)^2 = 16p^2$ (since $4p \times 4p = 16p^2$ ) $\newline$ $2(4p)(2) = 16p$ (since $2 \times 4p \times 2 = 16p$ ) $\newline$ $2^2 = 4$ (since $2 \times 2 = 4$ )
Combine Simplified Terms: Combine the simplified terms to get the final answer. $\newline$ $(4p + 2)^2 = 16p^2 + 16p + 4$

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