Question
Factorise: $12a^2b + 15ab^2$
✓
Answer
We have $12a^2b = 2 \times 2 \times 3 \times a \times a \times b $
$ 15ab^2= 3 \times 5 \times a \times b \times b$
The two terms have $3, a$ and $b$ as common factors.
Therefore, $12a^2b + 15ab^2= (3 \times a \times b \times 2 \times 2 \times a) + (3 \times a \times b \times 5 \times b)$
$= 3 \times a \times b \times [(2 \times 2 \times a) + (5 \times b)]$ (combining the terms)
$= 3ab \times (4a + 5b)$
$= 3ab (4a + 5b)$ (required factor form)
$ 15ab^2= 3 \times 5 \times a \times b \times b$
The two terms have $3, a$ and $b$ as common factors.
Therefore, $12a^2b + 15ab^2= (3 \times a \times b \times 2 \times 2 \times a) + (3 \times a \times b \times 5 \times b)$
$= 3 \times a \times b \times [(2 \times 2 \times a) + (5 \times b)]$ (combining the terms)
$= 3ab \times (4a + 5b)$
$= 3ab (4a + 5b)$ (required factor form)
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