The correct option is
A 8x2+30xy+27y2We need to find the value of the product
(2x+3y)(4x+9y) using FOIL rule.
Step 1:––––––––
We would multiply the "FIRST" terms in the product
(2x+3y)(4x+9y), i.e.,
2x and
4x.
2x×4x=8x1+1=8x2 (∵am×an=am+n)
The value of the first term in the product
(2x+3y)(4x+9y) is
8x2.
Step 2:––––––––
Now, we would multiply the "OUTER" terms in the product
(2x+3y)(4x+9y), i.e.,
2x and
9y.
2x×9y=18xy
The value of the second term in the product
(2x+3y)(4x+9y) is
18xy.
Step 3:––––––––
Now, we would multiply the "INNER" terms in the product
(2x+3y)(4x+9y), i.e.,
3y and
4x.
3y×4x=12xy
The value of third term in the product
(2x+3y)(4x+9y) is
12xy.
Step 4:––––––––
Now, we would multiply the "LAST" terms in the product
(2x+3y)(4x+9y), i.e.,
3y and
9y.
3y×9y=27y(1+1)=27y2 (∵am×an=am+n)
The value of fourth term in the product
(2x+3y)(4x+9y) is
27y2.
Step 5:––––––––
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
=8x2+18xy+12xy+27y2
=8x2+18xy+12xy––––––––––––––+27y2 (As
18xy and
12xy are like terms.)
=8x2+30xy+27y2
The value of the product
(2x+3y)(4x+9y) is
8x2+30xy+27y2.
Therefore, option (a.) is the correct answer.