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

Understand Binomial Theorem: We need to find the square of the binomial (w - 4). This is in the form of (a - b)^2, which is a special case of the binomial theorem. 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 (w - 4)^2. Compare (w - 4)^2 with (a - b)^2. a = w b = 4Apply Binomial Formula: Apply the square of a binomial formula to expand (w - 4)^2. (a - b)^2 = a^2 - 2ab + b^2 (w - 4)^2 = w^2 - 2(w)(4) + 4^2Simplify the Expression: Simplify w^2 - 2(w)(4) + 4^2. w^2 - 2(w)(4) + 4^2 = w^2 - (2 * 4)w + 4 * 4 = w^2 - 8w + 16

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

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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

(w - 4)^2

Understand Binomial Theorem: We need to find the square of the binomial $(w - 4)$ . This is in the form of $(a - b)^2$ , which is a special case of the binomial theorem. $\newline$ 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 $(w - 4)^2$ . Compare $(w - 4)^2$ with $(a - b)^2$ . $a = w$ $b = 4$
Apply Binomial Formula: Apply the square of a binomial formula to expand $(w - 4)^2$ . $\newline$ $(a - b)^2 = a^2 - 2ab + b^2$ $\newline$ $(w - 4)^2 = w^2 - 2(w)(4) + 4^2$
Simplify the Expression: Simplify $w^2 - 2(w)(4) + 4^2$ . $w^2 - 2(w)(4) + 4^2$ = $w^2 - (2 \times 4)w + 4 \times 4$ = $w^2 - 8w + 16$