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Factor. $\newline$ $4m^2 + 12m + 9$

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Factor quadratics: special cases

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Q. Factor.

\newline

4m^2 + 12m + 9

Check for Perfect Square Trinomial: Determine if the quadratic expression can be factored as a perfect square trinomial. A perfect square trinomial is in the form $(a + b)^2 = a^2 + 2ab + b^2$ . We need to check if $4m^2 + 12m + 9$ fits this pattern.
Identify $a^2$ , $2ab$ , $b^2$ : Identify $a^2$ , $2ab$ , and $b^2$ in the expression $4m^2 + 12m + 9$ . $\newline$ $a^2 = 4m^2$ , which suggests that $a = 2m$ . $\newline$ $b^2 = 9$ , which suggests that $2ab$ $0$ . $\newline$ To fit the pattern, $2ab$ should equal $2ab$ $2$ .
Verify $2ab$ Calculation: Verify that $2ab$ equals $12m$ using the values of $a$ and $b$ identified in Step $2$ . $\newline$ $2ab = 2 \times 2m \times 3 = 12m.$ $\newline$ This matches the middle term of the quadratic expression, confirming that it is a perfect square trinomial.
Write Factored Form: Write the factored form of the quadratic expression using the values of $a$ and $b$ . Since $a = 2m$ and $b = 3$ , the factored form is $(a + b)^2 = (2m + 3)^2$ .

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