Factor. 25x^2 - 20x + 4 ______

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 - 20x + 4 fits this pattern. 25x^2 can be written as (5x)^2, and 4 can be written as 2^2. The middle term, -20x, should be equal to 2 * 5x * 2 to fit the pattern. 2 * 5x * 2 = 20x, which matches the middle term except for the sign. So, 25x^2 - 20x + 4 is a perfect square trinomial.Factor Using Formula: Factor the expression using the perfect square trinomial formula. Since we have (5x)^2 - 2 * 5x * 2 + 2^2, the factored form will be (5x - 2)^2.Write Final Form: Write down the final factored form of the quadratic expression. The factored form of 25x^2 - 20x + 4 is (5x - 2)^2.

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Algebra 1

Factor quadratics: special cases

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Q. Factor.

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25x^2 - 20x + 4

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 $25x^2 - 20x + 4$ fits this pattern. $\newline$ $25x^2$ can be written as $(5x)^2$ , and $4$ can be written as $2^2$ . $\newline$ The middle term, $-20x$ , should be equal to $2 \times 5x \times 2$ to fit the pattern. $\newline$ $2 \times 5x \times 2 = 20x$ , which matches the middle term except for the sign. $\newline$ So, $25x^2 - 20x + 4$ is a perfect square trinomial.
Factor Using Formula: Factor the expression using the perfect square trinomial formula. $\newline$ Since we have $(5x)^2 - 2 \times 5x \times 2 + 2^2$ , the factored form will be $(5x - 2)^2$ .
Write Final Form: Write down the final factored form of the quadratic expression. $\newline$ The factored form of $25x^2 - 20x + 4$ is $(5x - 2)^2$ .