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Factor. $\newline$ $9h^2 + 6h + 1$

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Factor quadratics: special cases

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Q. Factor.

\newline

9h^2 + 6h + 1

Check 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 $(a^2 + 2ab + b^2) = (a + b)^2$ . We need to check if $9h^2 + 6h + 1$ fits this pattern. $\newline$ $9h^2$ is a perfect square, as $(3h)^2 = 9h^2$ . $\newline$ $1$ is a perfect square, as $1^2 = 1$ . $\newline$ The middle term, $6h$ , is twice the product of the square roots of the first and last terms, as $2 \times 3h \times 1 = 6h$ . $\newline$ Thus, the expression is a perfect square trinomial.
Factor Using Formula: Factor the expression using the perfect square trinomial formula. $\newline$ Since we have identified that $9h^2 + 6h + 1$ is a perfect square trinomial, we can write it as the square of a binomial. $\newline$ $(3h)^2 + 2 \times 3h \times 1 + 1^2 = (3h + 1)^2$ . $\newline$ Therefore, the factored form of $9h^2 + 6h + 1$ is $(3h + 1)(3h + 1)$ or $(3h + 1)^2$ .

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