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

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Factor quadratics: special cases

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Q. Factor.

\newline

25q^2 + 40q + 16

Identify Perfect Square Trinomial: Determine if the quadratic expression can be factored using the perfect square trinomial formula. $\newline$ A perfect square trinomial is in the form of $(a^2 + 2ab + b^2)$ which factors to $(a + b)^2$ . $\newline$ We can check if $25q^2 + 40q + 16$ is a perfect square trinomial by identifying $a^2$ , $2ab$ , and $b^2$ in the expression. $\newline$ $25q^2$ is a perfect square since $(5q)^2 = 25q^2$ . $\newline$ $16$ is a perfect square since $4^2 = 16$ . $\newline$ The middle term, $(a + b)^2$ $0$ , should be equal to $2ab$ . Since $(a + b)^2$ $2$ and $(a + b)^2$ $3$ , we have $(a + b)^2$ $4$ . $\newline$ Since all conditions for a perfect square trinomial are met, we can conclude that $25q^2 + 40q + 16$ is a perfect square trinomial.
Check for Perfect Square Trinomial: Factor the perfect square trinomial using the formula $(a + b)^2 = a^2 + 2ab + b^2$ . We have identified $a = 5q$ and $b = 4$ in the previous step. Therefore, the factored form of $25q^2 + 40q + 16$ is $(5q + 4)^2$ .

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