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Addition and Subtraction of Algebraic Expression

ix Simplify a...

Question

Question 84 (ix)

Simplify

$(a - b) (a^{2} + b^{2} + a b) - (a + b) (a^{2} + b^{2} - a b)$

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Solution

$(a - b) (a^{2} + b^{2} + a b) - (a + b) (a^{2} + b^{2} - a b) = a (a^{2} + b^{2} + a b) - b (a^{2} + b^{2} + a b) - a (a^{2} + b^{2} - a b) - b (a^{2} + b^{2} - a b) = a^{3} + a b^{2} + a^{2} b - b a^{2} - b^{3} - a b^{2} - a^{3} - a b^{2} + a^{2} b - b a^{2} - b^{3} + a b^{2} = (a^{3} - a^{3}) + (- b^{3} - b^{3}) + (a b^{2} - a b^{2}) + (a^{2} b - a^{2} b + a b^{2} - a b^{2}) = 0 - 2 b^{3} + 0 + 0 + 0 = - 2 b^{3}$

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Question 84 (ix)

Simplify

$(a - b) (a^{2} + b^{2} + a b) - (a + b) (a^{2} + b^{2} - a b)$

a^{3} - b^{3}

.

$(a + b) (a^{2} + b^{2} - a b)$ =

(a - b) (a^{2} + a b + b^{2})

{(a + b)}^{5} - a^{5} - b^{5} = 5 a b (a + b) (a^{2} + a b + b^{2})

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Addition and Subtraction of Algebraic Expression

Standard VIII Mathematics

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