Factor. 9s^2 + 30s + 25 ______

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) which factors to (a + b)^2. Check if 9s^2 + 30s + 25 fits this pattern. 9s^2 is a perfect square, as (3s)^2 = 9s^2. 25 is a perfect square, as 5^2 = 25. The middle term, 30s, is twice the product of the square roots of the first and last terms, as 2 * 3s * 5 = 30s. Since all conditions are met, we can conclude that 9s^2 + 30s + 25 is a perfect square trinomial.Identify a and b: Factor the perfect square trinomial using the formula (a + b)^2 = a^2 + 2ab + b^2. Identify a and b from the expression 9s^2 + 30s + 25. a = 3s (since (3s)^2 = 9s^2) b = 5 (since 5^2 = 25) Now, factor the expression as (a + b)^2. (3s + 5)^2 = (3s)^2 + 2 * 3s * 5 + 5^2 This matches the original expression, so the factored form is (3s + 5)^2.

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Algebra 1

Factor quadratics: special cases

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Q. Factor.

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9s^2 + 30s + 25

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 $(a^2 + 2ab + b^2)$ which factors to $(a + b)^2$ . $\newline$ Check if $9s^2 + 30s + 25$ fits this pattern. $\newline$ $9s^2$ is a perfect square, as $(3s)^2 = 9s^2$ . $\newline$ $25$ is a perfect square, as $5^2 = 25$ . $\newline$ The middle term, $30s$ , is twice the product of the square roots of the first and last terms, as $2 \times 3s \times 5 = 30s$ . $\newline$ Since all conditions are met, we can conclude that $9s^2 + 30s + 25$ is a perfect square trinomial.
Identify $a$ and $b$ : Factor the perfect square trinomial using the formula $(a + b)^2 = a^2 + 2ab + b^2$ . Identify $a$ and $b$ from the expression $9s^2 + 30s + 25$ . $a = 3s$ (since $(3s)^2 = 9s^2$ ) $b = 5$ (since $5^2 = 25$ ) Now, factor the expression as $b$ $0$ . $b$ $1$ This matches the original expression, so the factored form is $b$ $2$ .