Question

Factorise:$4y^2-9$

• A. (7y− 5)²
• B. (5y− 3)²
• C. (2y− 3)²
• D. (2y− 5)²

Answer 1

The correct option is C

(2y− 3)²

The expression $4y^2-9$ can be written as

$(2y{)}^2-3^2$.....(i)

Comparing (i) with the identity $(a{)}^2-(b{)}^2=(a+b)(a-b)$, we get

$a^2=(2y{)}^2\Rightarrow a=2y$

$b^2=3^2\Rightarrow b=3$

$\Rightarrow (2y{)}^2-3^2=(2y+3\left)\right(2y-3)$

Therefore, the factors of $4y^2-9$ are $(2y+3)$ and $(2y-3)$.

i.e., $4y^2-9=(2y{)}^2-3^2=(2y+3\left)\right(2y-3)$