Question

$\text{Factorise:}9x^2-24x+16$

• A. $(3x-4{)}^2$
• B. $(3x+4{)}^2$
• C. $(6x-4{)}^2$
• D. $(6x+4{)}^2$

Answer 1

The correct option is A $(3x-4{)}^2$

The given expression can be written as,
$9x^2-24x+16$
$=(3x{)}^2-2(3x\left)\right(4)+4^2$
Comparing the above equation with the identity
$(a-b{)}^2=a^2-2ab+b^2,$ we get
$9x^2-24x+16=(3x-4{)}^2$