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Sum

Expand a^{3}b^{2}, a^{2}b^{3}, b^{2}a^{3}, b^{3}a^{2}. Are they all same?

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#### Solution

a^{3}b^{2} = a^{3} × b^{2 }= (a × a × a) × (b × b) = a × a × a × b × b

a^{2}b^{3} = a^{2} × b^{3 }= a × a × b × b × b

b^{2}a^{3} = b^{2} × a^{3 }= b × b × a × a × a

b^{3}a^{2} = b^{3} × a^{2 }= b × b × b × a × a

a^{3}b^{2} and a^{2}b^{3} the powers of a and b are different. Thus a^{3}b^{2} and a^{2}b^{3} are different.

a^{3}b^{2} and b^{2}a^{3} are the same, since the powers of a and b in thesetwo terms are the same. The order of factors does not matter.

Thus, a^{3}b^{2} = a^{3} × b^{2} = b^{2} × a^{3} = b^{2}a^{3}. Similarly, a^{2}b^{3} and b^{3}a^{2} are the same.

Concept: Concept of Exponents

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