Question

The value of the product $6xy\times 12x^2{y}^2$ is same as the value of product?

• A. $72x^2{y}^2$
• B. $12xy\times 6xy$
• C. $12x^2{y}^2\times 6xy$
• D. $12x^2{y}^2\times 6x^2{y}^2$

Answer 1

The correct option is C $12x^2{y}^2\times 6xy$

The value of the product $6xy\times 12x^2{y}^2$ can be evaluated as:

$6xy\times 12x^2{y}^2$
$=(6\times 12)\times (xy\times x^2{y}^2)$
$=72x^{1+2}{y}^{1+2}(\because a^m\times a^n=a^{m+n})$
$=72x^3{y}^3$
The value of the product $6xy\times 12x^2{y}^2$ is $72x^3{y}^3$.

In option (a.), we have $72x^2{y}^2$.
$72x^2{y}^2\ne 72x^3{y}^3$
Therefore, option (a.) is not the correct answer.

In option (b.), we have $12xy\times 6xy$.
This product can be evaluated as:

$12xy\times 6xy=(12\times 6)\times (xy\times xy)$
$=72\times x^2{y}^2$
$=72x^2{y}^2$
But, $72x^2{y}^2\ne 72x^3{y}^3$
Therefore, option (b.) is not the correct answer.

In option (c.), we have $12x^2{y}^2\times 6xy$. This product can be evaluated as:

$12x^2{y}^2\times 6xy$
$=(12\times 6)\times (x^2{y}^2\times xy)$
$=72\times \left(x^{2+1}{y}^{2+1}\right)(a^m\times a^n=a^{m+n})$
$=72\times x^3{y}^3$
$=72x^3{y}^3$

The value obtained is the same as that of the value obtained of the product $6xy\times 12x^2{y}^2$.
Hence,
$6xy\times 12x^2{y}^2=12x^2{y}^2\times 6xy$
Therefore, option (c) is not the correct answer.

In option (d.), we have $12x^2{y}^2\times 6x^2{y}^2$. This product can be evaluated as:

$12x^2{y}^2\times 6x^2{y}^2$
$=(12\times 6)\times (x^2{y}^2\times x^2{y}^2)$
$=72\times \left(x^{2+2}{y}^{2+2}\right)(\because a^m\times a^n=a^{m+n})$
$=72\times x^4{y}^4$
$=72x^4{y}^4$
But, $72x^4{y}^4\ne 72x^2{y}^2$
Therefore, option (d.) is not the correct answer.

Alternate solution:
Multiplication is commutative i.e $a\times b=b\times a$
So,
$6xy\times 12x^2{y}^2=12x^2{y}^2\times 6xy$