Factor. 25t^2 + 10t + 1 ______

Identify Perfect Square Trinomial: Determine if the quadratic expression can be factored using the perfect square trinomial formula. A perfect square trinomial is in the form (at)^2 + 2abt + b^2, which factors to (at + b)^2. Check if 25t^2 + 10t + 1 fits this pattern. 25t^2 can be written as (5t)^2, and 1 can be written as (1)^2. The middle term, 10t, is 2 times 5t times 1. So, 25t^2 + 10t + 1 is a perfect square trinomial.Check Pattern: Factor the expression using the perfect square trinomial formula. Since we have identified that 25t^2 + 10t + 1 is a perfect square trinomial, it can be factored as: (5t + 1)^2

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Math Problems

Algebra 1

Factor quadratics: special cases

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Q. Factor.

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25t^2 + 10t + 1

Identify Perfect Square Trinomial: Determine if the quadratic expression can be factored using the perfect square trinomial formula. $\newline$ A perfect square trinomial is in the form $(at)^2 + 2abt + b^2$ , which factors to $(at + b)^2$ . $\newline$ Check if $25t^2 + 10t + 1$ fits this pattern. $\newline$ $25t^2$ can be written as $(5t)^2$ , and $1$ can be written as $(1)^2$ . $\newline$ The middle term, $10t$ , is $2$ times $5t$ times $1$ . $\newline$ So, $25t^2 + 10t + 1$ is a perfect square trinomial.
Check Pattern: Factor the expression using the perfect square trinomial formula. $\newline$ Since we have identified that $25t^2 + 10t + 1$ is a perfect square trinomial, it can be factored as: $\newline$ $(5t + 1)^2$