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Factor. $\newline$ $25s^2 + 40s + 16$

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Factor quadratics: special cases

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Q. Factor.

\newline

25s^2 + 40s + 16

Identify Quadratic Form: Identify the quadratic in the form of $ax^2 + bx + c$ . Here, $a = 25$ , $b = 40$ , and $c = 16$ .
Find Multiplying Numbers: Look for two numbers that multiply to $ac$ ( $25 \times 16 = 400$ ) and add up to $b$ ( $40$ ). $\newline$ The numbers are $20$ and $20$ because $20 \times 20 = 400$ and $20 + 20 = 40$ .
Rewrite Middle Term: Rewrite the middle term using the two numbers found. $\newline$ $25s^2 + 20s + 20s + 16$
Factor by Grouping: Factor by grouping. $\newline$ $(25s^2 + 20s) + (20s + 16)$
Factor Common Factor: Factor out the common factor from each group. $\newline$ $5s(5s + 4) + 4(5s + 4)$
Factor Common Binomial: Factor out the common binomial factor. $\newline$ $(5s + 4)(5s + 4)$

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