Question

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

Answer 1

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.