Factor completely. 25x^(2)-30 x+9=

Determine if perfect square trinomial: Determine if the quadratic expression is a perfect square trinomial. A perfect square trinomial is in the form (ax)^2 + 2abx + b^2, which factors to (ax + b)^2. For the given expression, 25x^2 - 30x + 9, we can compare it to the perfect square trinomial form: (5x)^2 - 2(5x)(3) + (3)^2Check pattern of perfect square trinomial: Check if the given expression fits the perfect square trinomial pattern. (5x)^2 = 25x^2 (which matches the first term of the given expression) 2(5x)(3) = 30x (which matches the middle term of the given expression, but with a negative sign) (3)^2 = 9 (which matches the last term of the given expression) Since the signs match the pattern of a perfect square trinomial, except the middle term has a negative sign, we can write the expression as: (5x - 3)^2Write factored form of expression: Write the factored form of the expression. The factored form of the expression 25x^2 - 30x + 9 is (5x - 3)^2.

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Math Problems

Algebra 1

Factor quadratics: special cases

Full solution

Q. Factor completely.

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25x^{2}-30x+9=

Determine if perfect square trinomial: Determine if the quadratic expression is a perfect square trinomial. $\newline$ A perfect square trinomial is in the form $(ax)^2 + 2abx + b^2$ , which factors to $(ax + b)^2$ . $\newline$ For the given expression, $25x^2 - 30x + 9$ , we can compare it to the perfect square trinomial form: $\newline$ $(5x)^2 - 2(5x)(3) + (3)^2$
Check pattern of perfect square trinomial: Check if the given expression fits the perfect square trinomial pattern. $\newline$ $(5x)^2 = 25x^2$ (which matches the first term of the given expression) $\newline$ $2(5x)(3) = 30x$ (which matches the middle term of the given expression, but with a negative sign) $\newline$ $(3)^2 = 9$ (which matches the last term of the given expression) $\newline$ Since the signs match the pattern of a perfect square trinomial, except the middle term has a negative sign, we can write the expression as: $\newline$ $(5x - 3)^2$
Write factored form of expression: Write the factored form of the expression. $\newline$ The factored form of the expression $25x^2 - 30x + 9$ is $(5x - 3)^2$ .