Find the square. Simplify your answer. (4z - 4)^2 ______

Identify binomial and formula: Identify the binomial to be squared and the special case formula to use. The given expression is (4z - 4)^2, which is in the form of (a - b)^2. Special case: (a - b)^2 = a^2 - 2ab + b^2Identify values of a and b: Identify the values of a and b in the binomial. Compare (4z - 4)^2 with (a - b)^2. a = 4z b = 4Apply binomial square formula: Apply the square of a binomial formula to expand (4z - 4)^2. (a - b)^2 = a^2 - 2ab + b^2 (4z - 4)^2 = (4z)^2 - 2(4z)(4) + 4^2Simplify expanded expression: Simplify the expanded expression. (4z)^2 - 2(4z)(4) + 4^2 = (4z * 4z) - (2 * 4 * 4)z + 4 * 4 = 16z^2 - 32z + 16

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Find the square. Simplify your answer. $\newline$ $(4z - 4)^2$

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Math Problems

Algebra 1

Multiply two binomials: special cases

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Q. Find the square. Simplify your answer.

\newline

(4z - 4)^2

Identify binomial and formula: Identify the binomial to be squared and the special case formula to use. $\newline$ The given expression is $(4z - 4)^2$ , which is in the form of $(a - b)^2$ . $\newline$ Special case: $(a - b)^2 = a^2 - 2ab + b^2$
Identify values of $a$ and $b$ : Identify the values of $a$ and $b$ in the binomial. Compare $(4z - 4)^2$ with $(a - b)^2$ . $a = 4z$ $b = 4$
Apply binomial square formula: Apply the square of a binomial formula to expand $(4z - 4)^2$ . $\newline$ $(a - b)^2 = a^2 - 2ab + b^2$ $\newline$ $(4z - 4)^2 = (4z)^2 - 2(4z)(4) + 4^2$
Simplify expanded expression: Simplify the expanded expression. $\newline$ $(4z)^2 - 2(4z)(4) + 4^2$ $\newline$ = $(4z \cdot 4z) - (2 \cdot 4 \cdot 4)z + 4 \cdot 4$ $\newline$ = $16z^2 - 32z + 16$