Factor by grouping.
\[
5 x-7+15 a x-21 a
\]

Answer

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Answer

\(\boxed{(1 + 3a)(5x - 7)}\) is the factored form of the given expression

Steps

Step 1 ：Rearrange the terms in the expression: \(5x + 15ax - 7 - 21a\)

Step 2 ：Group the terms: \((5x + 15ax) - (7 + 21a)\)

Step 3 ：Factor out the common factors from each group: \(5x(1 + 3a) - 7(1 + 3a)\)

Step 4 ：Factor out the common factor \((1 + 3a)\) from both terms: \((1 + 3a)(5x - 7)\)

Step 5 ：Check the work by expanding the factored form: \((1 + 3a)(5x - 7) = 5x - 7 + 15ax - 21a\)

Step 6 ：\(\boxed{(1 + 3a)(5x - 7)}\) is the factored form of the given expression