Question

Expand a³b² and a²b³ are they equal ?

Answer 1

We have:

$a^3b^2$ and $a^2b^3$

We have to expand  $a^3b^2$ and $a^2b^3$ and verify they are equal or not.

Solution:

∴ $a^3b^2$

To expand:

= (a × a × a)(b × b)

Also:

$a^2b^3$

To expand:

= (a × a)(b × b × b)

∵ $a^3b^2$ and $a^2b^3$ are not equal.

Thus,  $a^3b^2$ and $a^2b^3$ are not equal.

Answer 2

Given:

a³b² and a²b³

To find:

Expand a³b² and a²b³ are they equal?

Solution:

From given, we have the data as follows.

a³b² and a²b³

Firstly, we will expand the above terms one by one, and then we will continue with the comparison purpose.

So, we have,

a³b²

= (a × a × a) × (b × b)

So, in this term, there are 3 a's and 2 b's.

Now, consider the second term.

a²b³

= (a × a) × (b × b × b)

So, in this term, there are 2 a's and 3 b's.

As these are not the same, so, are different and are not equal.