Question

Factorise: $a^2(b+c)-(b+c{)}^3$

• A. $(b+c)\left[\right(a-b-c\left)\right(a+b+c\left)\right]$
• B. $(b-c)\left[\right(a-b-c\left)\right(a-b+c\left)\right]$
• C. $(b+c)\left[\right(a+b-c\left)\right(a+b+c\left)\right]$
• D. $(b+c)\left[\right(a-b+c\left)\right(a-b+c\left)\right]$

Answer 1

The correct option is A $(b+c)\left[\right(a-b-c\left)\right(a+b+c\left)\right]$

$a^2(b+c)-(b+c{)}^3$
=$(b+c)\left[\right(a^2-(b+c{)}^2]$
$[\because x^2-y^2=(x+y\left)\right(x-y\left)\right]$
=$(b+c)\left[\right(a-(b+c)\left)\right(a+(b+c)\left)\right]$
=$(b+c)\left[\right(a-b-c\left)\right(a+b+c\left)\right]$