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Factor. $\newline$ $4t^2 + 4t + 1$

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Factor quadratics: special cases

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Q. Factor.

\newline

4t^2 + 4t + 1

Identify Perfect Square Trinomial: Identify if the quadratic is a perfect square trinomial. $\newline$ $4t^2 = (2t)^2$ , $1 = (1)^2$ , and the middle term $4t$ is $2$ times $2t$ times $1$ . $\newline$ So, $4t^2 + 4t + 1$ is a perfect square trinomial.
Use Trinomial Formula: Use the perfect square trinomial formula $(a + b)^2 = a^2 + 2ab + b^2$ to factor. $(2t + 1)^2 = 4t^2 + 4t + 1$ .
Write Factored Form: Write the factored form of the expression. $\newline$ The factored form of $4t^2 + 4t + 1$ is $(2t + 1)(2t + 1)$ or $(2t + 1)^2$ .

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