Question

Evaluate the product $(2x+3y)(4x+9y)$ using FOIL rule.

• A. $8x^2+30xy+27y^2$
• B. $8x^2+6xy+27y^2$
• C. $8x^2-30xy+27y^2$
• D. $8x^2+30xy-27y^2$

Answer 1

The correct option is A $8x^2+30xy+27y^2$

We need to find the value of the product $(2x+3y)(4x+9y)$ using FOIL rule.

$\underset{–}{Step1:}$

We would multiply the "FIRST" terms in the product $(2x+3y)(4x+9y)$, i.e., $2x$ and $4x.$

$2x\times 4x=8x^{1+1}=8x^2$ $(\because a^m\times a^n=a^{m+n})$

The value of the first term in the product $(2x+3y)(4x+9y)$ is $8x^2$.


$\underset{–}{Step2:}$

Now, we would multiply the "OUTER" terms in the product $(2x+3y)(4x+9y)$, i.e., $2x$ and $9y.$


$2x\times 9y=18xy$

The value of the second term in the product $(2x+3y)(4x+9y)$ is $18xy$.


$\underset{–}{Step3:}$

Now, we would multiply the "INNER" terms in the product $(2x+3y)(4x+9y)$, i.e., $3y$ and $4x.$



$3y\times 4x=12xy$

The value of third term in the product $(2x+3y)(4x+9y)$ is $12xy$.


$\underset{–}{Step4:}$

Now, we would multiply the "LAST" terms in the product $(2x+3y)(4x+9y)$, i.e., $3y$ and $9y.$



$3y\times 9y=27y^{(1+1)}=27y^2$ $(\because a^m\times a^n=a^{m+n})$

The value of fourth term in the product $(2x+3y)(4x+9y)$ is $27y^2$.


$\underset{–}{Step5:}$
The value of product would be obtained by adding all the terms.
Product $=$ First term $+$ Second term $+$ Third term $+$ Fourth term

Hence, $(2x+3y)(4x+9y)$ is
$=8x^2+18xy+12xy+27y^2$
$=8x^2+\underset{–}{18xy+12xy}+27y^2$ (As $18xy$ and $12xy$ are like terms.)
$=8x^2+30xy+27y^2$

The value of the product $(2x+3y)(4x+9y)$ is $8x^2+30xy+27y^2$.
Therefore, option (a.) is the correct answer.