Factor. 16g^2 + 8g + 1 ______

Check for Perfect Square Trinomial: Determine if the quadratic can be factored as a perfect square trinomial. A perfect square trinomial is in the form (ag + b)^2 = a^2g^2 + 2abg + b^2. We need to check if 16g^2 + 8g + 1 fits this pattern.Identify Square Roots: Identify the square root of the first term and the last term. The square root of 16g^2 is 4g, and the square root of 1 is 1. So, we will check if the middle term, 8g, is twice the product of 4g and 1. 2 * 4g * 1 = 8g, which matches the middle term.Write as Perfect Square Trinomial: Write the expression as a perfect square trinomial. Since the middle term is twice the product of the square roots of the first and last terms, the expression can be written as (4g + 1)^2.

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Algebra 1

Factor quadratics: special cases

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Q. Factor.

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16g^2 + 8g + 1

Check for Perfect Square Trinomial: Determine if the quadratic can be factored as a perfect square trinomial. A perfect square trinomial is in the form $(ag + b)^2 = a^2g^2 + 2abg + b^2$ . We need to check if $16g^2 + 8g + 1$ fits this pattern.
Identify Square Roots: Identify the square root of the first term and the last term. $\newline$ The square root of $16g^2$ is $4g$ , and the square root of $1$ is $1$ . $\newline$ So, we will check if the middle term, $8g$ , is twice the product of $4g$ and $1$ . $\newline$ $2 \times 4g \times 1 = 8g$ , which matches the middle term.
Write as Perfect Square Trinomial: Write the expression as a perfect square trinomial. $\newline$ Since the middle term is twice the product of the square roots of the first and last terms, the expression can be written as $(4g + 1)^2$ .