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Find the square. Simplify your answer. $\newline$ $(4f + 1)^2$

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Multiply two binomials: special cases

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Q. Find the square. Simplify your answer.

\newline

(4f + 1)^2

Identify values of $a$ and $b$ : Identify the values of $a$ and $b$ in the binomial $(4f + 1)^2$ . Here, $a = 4f$ and $b = 1$ .
Apply binomial square formula: Apply the square of a binomial formula to expand $(4f + 1)^2$ . Using the formula $(a + b)^2 = a^2 + 2ab + b^2$ , we get: $(4f + 1)^2 = (4f)^2 + 2\cdot(4f)\cdot1 + 1^2$ .
Simplify each term: Simplify each term in the expansion. $\newline$ $(4f)^2 = 16f^2$ (since $4f \times 4f = 16f^2$ ), $\newline$ $2\times(4f)\times1 = 8f$ (since $2 \times 4f \times 1 = 8f$ ), $\newline$ $1^2 = 1$ (since $1 \times 1 = 1$ ).
Combine simplified terms: Combine the simplified terms to get the final answer. $\newline$ $(4f + 1)^2 = 16f^2 + 8f + 1$ .

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