Question

Factorise $a^2-81(b-c{)}^2$ is _____.

• A. $(a+b-9c)(a-9b+c)$
• B. $(a+b-c)(a-9b+9c)$
• C. $(a+9b-9c)(a-9b+9c)$
• D. $(9a+b-9c)(a-9b+c)$

Answer 1

The correct option is C $(a+9b-9c)(a-9b+9c)$

$a^2-81(b-c{)}^2$
$=a^2-\left(9\right(b-c){)}^2$
We know $a^2-b^2=(a+b)(a-b)$
$a^2-\left(9\right(b-c){)}^2$
$=\left[\right(a+9(b-c)\left]\right[a-9(b-c)]$
$=[a+9b-9c][a-9b+9c]$