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Factor. $\newline$ $y^2 + 4y + 4$

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Factor quadratics: special cases

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Q. Factor.

\newline

y^2 + 4y + 4

Identify Perfect Square Trinomial: Determine if the quadratic can be factored using the perfect square trinomial formula. $\newline$ A perfect square trinomial is in the form $(a + b)^2 = a^2 + 2ab + b^2$ . We need to check if $y^2 + 4y + 4$ fits this pattern. $\newline$ $y^2$ is a perfect square, as $y^2 = (y)^2$ . $\newline$ $4y$ is twice the product of $y$ and some number $b$ . $\newline$ $4$ is a perfect square, as $4 = 2^2$ . $\newline$ We can see that $4y$ is twice the product of $y$ and $y^2 + 4y + 4$ $1$ , which means $y^2 + 4y + 4$ $2$ . $\newline$ So, $y^2 + 4y + 4$ fits the pattern of a perfect square trinomial with $y^2 + 4y + 4$ $4$ and $y^2 + 4y + 4$ $5$ .
Apply Perfect Square Trinomial Formula: Factor the expression using the perfect square trinomial formula. $\newline$ Since we have identified that $y^2 + 4y + 4$ is a perfect square trinomial, we can write it as $(y + 2)^2$ . $\newline$ This is because $(y + 2)(y + 2) = y^2 + 2\cdot y\cdot 2 + 2^2 = y^2 + 4y + 4$ .

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