Find the square. Simplify your answer. (4f + 4)^2 ______

Identify Binomial and Formula: Identify the binomial to be squared and the special case formula to use. The given binomial is (4f + 4), and we need to square it. The special case formula for the square of a binomial (a + b)^2 is a^2 + 2ab + b^2.Identify a and b: Identify the values of a and b in the binomial. In the binomial (4f + 4), a is 4f and b is 4.Apply Binomial Formula: Apply the square of a binomial formula to expand (4f + 4)^2. Using the formula (a + b)^2 = a^2 + 2ab + b^2, we get: (4f + 4)^2 = (4f)^2 + 2(4f)(4) + (4)^2Simplify Expansion: Simplify each term in the expansion. (4f)^2 = 16f^2 (since 4f * 4f = 16f^2) 2(4f)(4) = 32f (since 2 * 4f * 4 = 32f) (4)^2 = 16 (since 4 * 4 = 16) So, (4f + 4)^2 = 16f^2 + 32f + 16

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Algebra 1

Multiply two binomials: special cases

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Q. Find the square. Simplify your answer.

\newline

(4f + 4)^2

Identify Binomial and Formula: Identify the binomial to be squared and the special case formula to use. $\newline$ The given binomial is $(4f + 4)$ , and we need to square it. The special case formula for the square of a binomial $(a + b)^2$ is $a^2 + 2ab + b^2$ .
Identify $a$ and $b$ : Identify the values of $a$ and $b$ in the binomial. $\newline$ In the binomial $(4f + 4)$ , $a$ is $4f$ and $b$ is $4$ .
Apply Binomial Formula: Apply the square of a binomial formula to expand $(4f + 4)^2$ . Using the formula $(a + b)^2 = a^2 + 2ab + b^2$ , we get: $(4f + 4)^2 = (4f)^2 + 2(4f)(4) + (4)^2$
Simplify Expansion: Simplify each term in the expansion. $\newline$ $(4f)^2 = 16f^2$ (since $4f \times 4f = 16f^2$ ) $\newline$ $2(4f)(4) = 32f$ (since $2 \times 4f \times 4 = 32f$ ) $\newline$ $(4)^2 = 16$ (since $4 \times 4 = 16$ ) $\newline$ So, $(4f + 4)^2 = 16f^2 + 32f + 16$