State the following statement is True or False:
$a^{3} - b^{3} = (a - b) (a^{2} + b^{2} + a b)$ .

True

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False

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Solution

The correct option is A True
Simplifying the expression on right hand side of the equation,
$(a - b) (a^{2} + b^{2} + a b)$ = $a^{3} + a b^{2} + a^{2} b - b a^{2} - b^{3} - a b^{2} = a^{3} - b^{3}$

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Similar questions

(\frac{x^{a}}{x^{- b}})^{a^{2} - a b + b^{2}} \times (\frac{x^{b}}{x^{- c}})^{b^{2} - b c + c^{2}} \times (\frac{x^{c}}{x^{- a}})^{c^{2} - c a + a^{2}} =

x^{2 (a^{3} + b^{3} + c^{3})}

a^{3} + b^{3} + c^{3} - 3 a b c = \frac{1}{2} (a + b + c) [(a - b)^{2} + (b - c)^{2} + (c - a)^{2}]

a^{3} - b^{3}

\sqrt{a^{3} b^{4}} \sqrt[3]{a^{4} b^{3}}

= a^{2} b^{3} \cdot {\sqrt[6]{a}}^{5}

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