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

Check Pattern: Determine if the quadratic expression can be factored using the perfect square trinomial formula. A perfect square trinomial is in the form (ax)^2 - 2abx + b^2, which factors to (ax - b)^2. Check if 25x^2 - 40x + 16 fits this pattern. 25x^2 can be written as (5x)^2, and 16 can be written as 4^2. The middle term, -40x, should be equal to 2 * 5x * 4 if it fits the pattern. Calculate 2 * 5x * 4 = 40x, which matches the middle term except for the sign.Factor Expression: Factor the expression using the perfect square trinomial formula. Since the expression fits the pattern of a perfect square trinomial, we can write it as: (5x)^2 - 2 * 5x * 4 + 4^2 This simplifies to: (5x - 4)^2

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Algebra 1

Factor quadratics: special cases

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Q. Factor.

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25x^2 - 40x + 16

Check Pattern: Determine if the quadratic expression can be factored using the perfect square trinomial formula. $\newline$ A perfect square trinomial is in the form $(ax)^2 - 2abx + b^2$ , which factors to $(ax - b)^2$ . $\newline$ Check if $25x^2 - 40x + 16$ fits this pattern. $\newline$ $25x^2$ can be written as $(5x)^2$ , and $16$ can be written as $4^2$ . $\newline$ The middle term, $-40x$ , should be equal to $2 \times 5x \times 4$ if it fits the pattern. $\newline$ Calculate $2 \times 5x \times 4 = 40x$ , which matches the middle term except for the sign.
Factor Expression: Factor the expression using the perfect square trinomial formula. $\newline$ Since the expression fits the pattern of a perfect square trinomial, we can write it as: $\newline$ $(5x)^2 - 2 \times 5x \times 4 + 4^2$ $\newline$ This simplifies to: $\newline$ $(5x - 4)^2$