Factorise : $3 a c + 7 b c - 3 a d - 7 b d$

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Solution

GIven that: $3 a c + 7 b c - 3 a d - 7 b d$
$= (3 a c + 7 b c) + (- 3 a d - 7 b d)$ , (group pair of terms)
$= c (3 a + 7 b) - d (3 a + 7 b)$ , (factor each binomials)
$= (3 a + 7 b) (c - d)$ , (factor out common factor $(3 a + 7 b)$ )
The factors of $3 a c + 7 b c - 3 a d - 7 b d$ are $(3 a + 7 b) (c - d)$

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