Factor. t^2 + 4t + 4 ______

Determine Approach: Determine the approach to factor the quadratic expression t^2 + 4t + 4. We can use the perfect square trinomial formula: (a + b)^2 = a^2 + 2ab + b^2, since the expression resembles a perfect square trinomial.Identify Values: Identify the values of a and b that would make the expression a perfect square trinomial. For the expression t^2 + 4t + 4, we can see that a = t and b = 2 because: a^2 = t^2 2ab = 2 * t * 2 = 4t b^2 = 2^2 = 4 So, t^2 + 4t + 4 is in the form of a^2 + 2ab + b^2.Factor Expression: Factor the expression using the perfect square trinomial formula. Since we have identified a = t and b = 2, we can write the factored form as: (t + 2)^2 This is because (t + 2)(t + 2) = t^2 + 2t + 2t + 4 = t^2 + 4t + 4.

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Algebra 1

Factor quadratics: special cases

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Q. Factor.

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t^2 + 4t + 4

Determine Approach: Determine the approach to factor the quadratic expression $t^2 + 4t + 4$ . We can use the perfect square trinomial formula: $(a + b)^2 = a^2 + 2ab + b^2$ , since the expression resembles a perfect square trinomial.
Identify Values: Identify the values of $a$ and $b$ that would make the expression a perfect square trinomial. $\newline$ For the expression $t^2 + 4t + 4$ , we can see that $a = t$ and $b = 2$ because: $\newline$ $a^2 = t^2$ $\newline$ $2ab = 2 \times t \times 2 = 4t$ $\newline$ $b^2 = 2^2 = 4$ $\newline$ So, $t^2 + 4t + 4$ is in the form of $a^2 + 2ab + b^2$ .
Factor Expression: Factor the expression using the perfect square trinomial formula. $\newline$ Since we have identified $a = t$ and $b = 2$ , we can write the factored form as: $\newline$ $(t + 2)^2$ $\newline$ This is because $(t + 2)(t + 2) = t^2 + 2t + 2t + 4 = t^2 + 4t + 4$ .