Question
Factorise:
$9(2 a-b)^2-4(2 a-b)-13$
$9(2 a-b)^2-4(2 a-b)-13$
✓
Answer
Let $2 a - b = c$
Then, $9(2 a-b)^2-4(2 a-b)-13$
$=9 c^2-4 c-13$
$=9 c^2-13 c+9 c-13$
$=c(9 c-13)+1(9 c-13)$
$=(c+1)(9 c-13)$
Now, replacing $c$ by ( $2 a - b )$, we get
$9(2 a-b)^2-4(2 a-b)-13$
$=(2 a-b+1)[9(2 a-b)-13]$
$=(2 a-b+1)(18 a-9 b-13)$
Then, $9(2 a-b)^2-4(2 a-b)-13$
$=9 c^2-4 c-13$
$=9 c^2-13 c+9 c-13$
$=c(9 c-13)+1(9 c-13)$
$=(c+1)(9 c-13)$
Now, replacing $c$ by ( $2 a - b )$, we get
$9(2 a-b)^2-4(2 a-b)-13$
$=(2 a-b+1)[9(2 a-b)-13]$
$=(2 a-b+1)(18 a-9 b-13)$
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