$Factorise a^{2} b - b^{3} . Using this result, find the value of 101^{2} \times 100 - 100^{3}$

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Solution

$a^{2} b - b^{3} b (a^{2} - b^{2}) b (a + b) (a - b) Now, 101^{2} \times 100 - 100^{3} = 100 (101^{2} - 100^{2}) = 100 (101 + 100) (101 - 100) = 100 (201) (1) = 20100$

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