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Question

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

A
8x2+30xy+27y2
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B
8x2+6xy+27y2
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C
8x230xy+27y2
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D
8x2+30xy27y2
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Solution

The correct option is A 8x2+30xy+27y2
We 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.

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