1. Calculate the H. C.F of a 2 b 5 and a 3 b 3 .

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  a^2·b^3

Step-by-step explanation:

Factors of both terms include 'a' to some power, and 'b' to some power. The greatest common factor will use the lowest power of each of these variables.

  powers of 'a' are a^2, a^3. Greatest common power is a^2

  powers of 'b' are b^5 and b^3. Greatest common power is b^3

The highest common factor of both terms is a^2·b^3.

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Additional comment

When that is factored out of the sum, you have ...

  a^2b^5 +a^3b^3 = a^2·b^3(b^2 +a)

The remaining two terms (b^2+a) have no common factors—as it should be.

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