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

Check 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. Check if 16x^2 + 40x + 25 fits this pattern. 16x^2 is a perfect square, as 16x^2 = (4x)^2. 25 is a perfect square, as 25 = 5^2. The middle term, 40x, is twice the product of the square roots of the first and last terms, as 2 * 4x * 5 = 40x. Since all conditions are met, the expression is a perfect square trinomial.Factor Trinomial: Factor the perfect square trinomial. Since we have established that the expression is a perfect square trinomial, we can factor it as (ax + b)^2. From Step 1, we know that a = 4x and b = 5. Therefore, the factored form is (4x + 5)^2.

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Algebra 1

Factor quadratics: special cases

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Q. Factor.

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16x^2 + 40x + 25

Check 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 $(ax + b)^2$ . $\newline$ Check if $16x^2 + 40x + 25$ fits this pattern. $\newline$ $16x^2$ is a perfect square, as $16x^2 = (4x)^2$ . $\newline$ $25$ is a perfect square, as $25 = 5^2$ . $\newline$ The middle term, $40x$ , is twice the product of the square roots of the first and last terms, as $2 \times 4x \times 5 = 40x$ . $\newline$ Since all conditions are met, the expression is a perfect square trinomial.
Factor Trinomial: Factor the perfect square trinomial. $\newline$ Since we have established that the expression is a perfect square trinomial, we can factor it as $(ax + b)^2$ . $\newline$ From Step $1$ , we know that $a = 4x$ and $b = 5$ . $\newline$ Therefore, the factored form is $(4x + 5)^2$ .