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

Approach Determination: Determine the approach to factor 9 - 25x^2. We can observe that both 9 and 25x^2 are perfect squares, and they are being subtracted from each other. This suggests that we can use the difference of squares formula, which is a^2 - b^2 = (a - b)(a + b).Identify Form: Identify 9 - 25x^2 in the form of a^2 - b^2. 9 can be written as 3^2, and 25x^2 can be written as (5x)^2. Therefore, we have: 9 - 25x^2 = 3^2 - (5x)^2Apply Formula: Apply the difference of squares formula. Using the formula a^2 - b^2 = (a - b)(a + b), we substitute a with 3 and b with 5x: 3^2 - (5x)^2 = (3 - 5x)(3 + 5x)Final Factored Form: Write the final factored form. The factored form of 9 - 25x^2 is (3 - 5x)(3 + 5x).

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Math Problems

Algebra 1

Factor quadratics: special cases

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Q. Factor completely.

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9-25x^{2}=

Approach Determination: Determine the approach to factor $9 - 25x^2$ . We can observe that both $9$ and $25x^2$ are perfect squares, and they are being subtracted from each other. This suggests that we can use the difference of squares formula, which is $a^2 - b^2 = (a - b)(a + b)$ .
Identify Form: Identify $9 - 25x^2$ in the form of $a^2 - b^2$ . $9$ can be written as $3^2$ , and $25x^2$ can be written as $(5x)^2$ . Therefore, we have: $9 - 25x^2 = 3^2 - (5x)^2$
Apply Formula: Apply the difference of squares formula. $\newline$ Using the formula $a^2 - b^2 = (a - b)(a + b)$ , we substitute $a$ with $3$ and $b$ with $5x$ : $\newline$ $3^2 - (5x)^2 = (3 - 5x)(3 + 5x)$
Final Factored Form: Write the final factored form. $\newline$ The factored form of $9 - 25x^2$ is $(3 - 5x)(3 + 5x)$ .