Factor. n^2 + 8n + 16 ______

Check Perfect Square Trinomial: Determine if the quadratic can be factored using the perfect square trinomial formula. A perfect square trinomial is in the form (a + b)^2 = a^2 + 2ab + b^2. We need to check if n^2 + 8n + 16 fits this pattern.Identify Square Roots: Identify the square root of the first term and the last term. The square root of n^2 is n, and the square root of 16 is 4. So, we have potential candidates for a and b in the perfect square trinomial formula: a = n and b = 4.Verify Middle Term: Check if the middle term fits the formula 2ab. For our candidates a = n and b = 4, the middle term should be 2 * n * 4 = 8n. This matches the middle term of our quadratic expression.Write Factored Form: Write the factored form using the perfect square trinomial formula. Since the expression fits the pattern of a perfect square trinomial, we can write it as (n + 4)^2.

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Math Problems

Algebra 1

Factor quadratics: special cases

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Q. Factor.

\newline

n^2 + 8n + 16

Check 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 $n^2 + 8n + 16$ fits this pattern.
Identify Square Roots: Identify the square root of the first term and the last term. $\newline$ The square root of $n^2$ is $n$ , and the square root of $16$ is $4$ . So, we have potential candidates for $a$ and $b$ in the perfect square trinomial formula: $a = n$ and $b = 4$ .
Verify Middle Term: Check if the middle term fits the formula $2ab$ . For our candidates $a = n$ and $b = 4$ , the middle term should be $2 \times n \times 4 = 8n$ . This matches the middle term of our quadratic expression.
Write Factored Form: Write the factored form using the perfect square trinomial formula. $\newline$ Since the expression fits the pattern of a perfect square trinomial, we can write it as $(n + 4)^2$ .