Factor. 25y^2 - 40y + 16 ______

Check 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 (a^2 ± 2ab + b^2) = (a ± b)^2. We can check if 25y^2 - 40y + 16 fits this pattern. 25y^2 is a perfect square, as (5y)^2 = 25y^2. 16 is a perfect square, as 4^2 = 16. The middle term, -40y, is twice the product of the square roots of the first and last terms, as 2 * 5y * 4 = 40y. Thus, the expression is a perfect square trinomial.Rewrite in Correct Form: Write the expression in the form of (a^2 - 2ab + b^2). The given expression is 25y^2 - 40y + 16. We can rewrite it as (5y)^2 - 2 * 5y * 4 + 4^2.Factor Using Formula: Factor the perfect square trinomial using the formula (a - b)^2. Since we have (5y)^2 - 2 * 5y * 4 + 4^2, we can factor it as (5y - 4)^2.

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Algebra 1

Factor quadratics: special cases

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Q. Factor.

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25y^2 - 40y + 16

Check 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 $(a^2 \pm 2ab + b^2) = (a \pm b)^2$ . $\newline$ We can check if $25y^2 - 40y + 16$ fits this pattern. $\newline$ $25y^2$ is a perfect square, as $(5y)^2 = 25y^2$ . $\newline$ $16$ is a perfect square, as $4^2 = 16$ . $\newline$ The middle term, $-40y$ , is twice the product of the square roots of the first and last terms, as $2 \times 5y \times 4 = 40y$ . $\newline$ Thus, the expression is a perfect square trinomial.
Rewrite in Correct Form: Write the expression in the form of $(a^2 - 2ab + b^2)$ . $\newline$ The given expression is $25y^2 - 40y + 16$ . $\newline$ We can rewrite it as $(5y)^2 - 2 \times 5y \times 4 + 4^2$ .
Factor Using Formula: Factor the perfect square trinomial using the formula $(a - b)^2$ . Since we have $(5y)^2 - 2 \times 5y \times 4 + 4^2$ , we can factor it as $(5y - 4)^2$ .