Expand a3 b2, a2 b3, b2 a3, b3 a2. Are they all same? - Mathematics

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Sum

Expand a3b2, a2b3, b2a3, b3a2. Are they all same?

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Solution

a3b2 = a3 × b2 = (a × a × a) × (b × b) = a × a × a × b × b

a2b3 = a2 × b3 = a × a × b × b × b

b2a3 = b2 × a3 = b × b × a × a × a

b3a2 = b3 × a2 = b × b × b × a × a

a3b2 and a2b3 the powers of a and b are different. Thus a3b2 and a2b3 are different.

a3b2 and b2a3 are the same, since the powers of a and b in thesetwo terms are the same. The order of factors does not matter.

Thus, a3b2 = a3 × b2 = b2 × a3 = b2a3. Similarly, a2b3 and b3a2 are the same.

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