Question

Factors of $18y^2+24xy+36y$ are:

• A. $6y$ and $(3+4y+6y)$
• B. $6$ and $(3y+4y+6)$
• C. $y$ and $(3y+4y+6)$
• D. $6y$ and $(3y+4x+6)$

Answer 1

The correct option is D

$6y$ and $(3y+4x+6)$

The expression $18y^2+24xy+36y$ can be written as,
$=2\times 3\times 3\times y\times y+3\times 2\times 2\times 2\times x\times y+2\times 2\times 3\times 3\times y$...(i)

Taking $6y$ common from (i), we get
$=3\times 2\times y(3\times y+2\times 2\times x+3\times 2)$
$=6y(3y+4x+6)$

$\Rightarrow$ $18y^2+24xy+36y$$=6y(3y+4x+6)$
So, $6y$ and $(3y+4x+6)$ are the two factors of the given expression.