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Factor. $\newline$ $9w^2 - 24w + 16$

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Factor quadratics: special cases

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Q. Factor.

\newline

9w^2 - 24w + 16

Identify Quadratic Expression: Identify the quadratic expression in the form of $aw^2 + bw + c$ . Here, $a = 9$ , $b = -24$ , and $c = 16$ .
Find Multiplying Numbers: Look for two numbers that multiply to $ac$ ( $9 \times 16 = 144$ ) and add up to $b$ ( $-24$ ). $\newline$ The numbers are $-12$ and $-12$ because $-12 \times -12 = 144$ and $-12 + -12 = -24$ .
Rewrite Middle Term: Rewrite the middle term $-24w$ using the two numbers found: $-12w$ and $-12w$ . So, $9w^2 - 24w + 16$ becomes $9w^2 - 12w - 12w + 16$ .
Factor by Grouping: Factor by grouping. Group the first two terms and the last two terms. $\newline$ $(9w^2 - 12w) - (12w - 16)$
Factor out Common Factor: Factor out the common factor from each group. $\newline$ $3w(3w - 4) - 4(3w - 4)$
Notice Common Factor: Notice that $(3w - 4)$ is a common factor. $\newline$ Factor out $(3w - 4)$ from both terms. $\newline$ $(3w - 4)(3w - 4)$

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