Factor

$t^{2} + 4 t + 4$

Step 1

Rewrite $4$ as $2^{2}$ .

$t^{2} + 4 t + 2^{2}$

Step 2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$4 t = 2 \cdot t \cdot 2$

Step 3

Rewrite the polynomial.

$t^{2} + 2 \cdot t \cdot 2 + 2^{2}$

Step 4

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = t$ and $b = 2$ .

${(t + 2)}^{2}$

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$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$