Question

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

• A. 2b(2a+3b)
• B. 3b(3a+2b)
• C. 3b(2a+3b)
• D. 3b(2a-3b)

Answer 1

The correct option is C 3b(2a+3b)

The given expression is $(a+3b{)}^2-a^2$
= $\left(\right(a+3b)-a)\left(\right(a+3b)+a)$ [Using the identity $a^2-b^2=(a+b)(a-b)$]

= (a+3b - a)(a+3b + a)
= 3b(2a+3b)