How do you factor $9 x^{2} - 25$ ?

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Solution

Find the factor of $9 x^{2} - 25$ :
The given expression is $9 x^{2} - 25$ .
The expression $9 x^{2} - 25$ can be written as ${(3 x)}^{2} - 5^{2}$ .
Use the following identity $a^{2} - b^{2} = (a + b) (a - b)$ and write the given expression as:
${(3 x)}^{2} - 5^{2} = (3 x + 5) (3 x - 5)$
Therefore, the factor of $9 x^{2} - 25$ is $(3 x + 5) (3 x - 5)$ .

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