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

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Multiply two binomials: special cases

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Q. Find the square. Simplify your answer.

\newline

(4r + 2)^2

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

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