Factor. 4p^2 + 12p + 9 ______

Check Perfect Square Trinomial: Determine if the quadratic 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 4p^2 + 12p + 9 fits this pattern. 4p^2 can be written as (2p)^2, and 9 can be written as 3^2. The middle term, 12p, should be 2 times the product of the square roots of the first and last terms if it is a perfect square trinomial. Let's check: 2 * (2p) * 3 = 12p, which matches the middle term.Write as Perfect Square: Write the quadratic as a perfect square trinomial. Since the quadratic fits the pattern of a perfect square trinomial, we can write it as: (2p + 3)^2 = (2p)^2 + 2*(2p)*3 + 3^2 This matches the original expression 4p^2 + 12p + 9.Factor Trinomial: Factor the perfect square trinomial. The factored form of the expression is simply the square of the binomial we identified: (2p + 3)^2 So, the factored form of 4p^2 + 12p + 9 is (2p + 3)(2p + 3) or (2p + 3)^2.

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Algebra 1

Factor quadratics: special cases

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Q. Factor.

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4p^2 + 12p + 9

Check Perfect Square Trinomial: Determine if the quadratic can be factored as a perfect square trinomial. $\newline$ A perfect square trinomial is in the form $(a + b)^2 = a^2 + 2ab + b^2$ . We need to check if $4p^2 + 12p + 9$ fits this pattern. $\newline$ $4p^2$ can be written as $(2p)^2$ , and $9$ can be written as $3^2$ . The middle term, $12p$ , should be $2$ times the product of the square roots of the first and last terms if it is a perfect square trinomial. $\newline$ Let's check: $2 \times (2p) \times 3 = 12p$ , which matches the middle term.
Write as Perfect Square: Write the quadratic as a perfect square trinomial. $\newline$ Since the quadratic fits the pattern of a perfect square trinomial, we can write it as: $\newline$ $(2p + 3)^2 = (2p)^2 + 2\cdot(2p)\cdot3 + 3^2$ $\newline$ This matches the original expression $4p^2 + 12p + 9$ .
Factor Trinomial: Factor the perfect square trinomial. $\newline$ The factored form of the expression is simply the square of the binomial we identified: $\newline$ $(2p + 3)^2$ $\newline$ So, the factored form of $4p^2 + 12p + 9$ is $(2p + 3)(2p + 3)$ or $(2p + 3)^2$ .