Question

Factorise: $5(a+b{)}^2+10(a^2-b^2)+5(a-b{)}^2$

• A. $5a^2$
• B. $20b^2$
• C. $20a^2$
• D. $4a^2$

Answer 1

The correct option is C $20a^2$

$5(a+b{)}^2+10(a^2-b^2)+5(a-b{)}^2$
$=5\left[\right(a+b{)}^2+2(a^2-b^2)+(a-b{)}^2$
$=5\left[\right(a+b)+(a-b){]}^2$
$[\because (a+b{)}^2=a^2+2ab+b^2]$
$=5[a+b+a-b{]}^2$
$=5(2a{)}^2$
$=20a^2$