Question

factor the expression.
$175x^2 - 1183$
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enter your answer
factor the expression.
$294 - 96b^2$
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Explanation:

For \(175x^2 - 1183\):

Step1: Factor out GCF

Find greatest common factor of 175 and 1183, which is 7.
\(175x^2 - 1183 = 7(25x^2 - 169)\)

Step2: Factor difference of squares

Recognize \(25x^2-169=(5x)^2-13^2\), use \(a^2-b^2=(a-b)(a+b)\).
\(7(25x^2 - 169) = 7(5x - 13)(5x + 13)\)

For \(294 - 96b^2\):

Step1: Factor out GCF

Find greatest common factor of 294 and 96, which is 6.
\(294 - 96b^2 = 6(49 - 16b^2)\)

Step2: Factor difference of squares

Recognize \(49-16b^2=7^2-(4b)^2\), use \(a^2-b^2=(a-b)(a+b)\).
\(6(49 - 16b^2) = 6(7 - 4b)(7 + 4b)\)

Answer:

1. \(7(5x - 13)(5x + 13)\)
2. \(6(7 - 4b)(7 + 4b)\)