We have (a+b)^3=a^3+b^3+3ab(a+b) and #160; (a b)^3=a^3 b^3 3ab(a b) ⇒(a+b)^3 (a b)^3 =a^3+b^3+3ab(a+b) a^3+b^3+3ab(a b) =a^3+b^3+3a^2 ...

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Quadratic Equations

Evaluate: a+...

Question

Evaluate: ${(a + b)}^{3} - {(a - b)}^{3}$

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Solution

We have ${(a + b)}^{3} = a^{3} + b^{3} + 3 a b (a + b)$ and

${(a - b)}^{3} = a^{3} - b^{3} - 3 a b (a - b)$

$\Rightarrow {(a + b)}^{3} - {(a - b)}^{3}$

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

$= a^{3} + b^{3} + 3 a^{2} b + 3 a b^{2} - a^{3} + b^{3} + 3 a^{2} b - 3 a b^{2}$

$= 2 b^{3} + 6 a^{2} b$

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Similar questions

Evaluate $\frac{a^{3} + b^{3} + c^{3} - 3 a b c}{(a + b + c)}, where (a + b + c) \neq 0$ .

(a + b)^{2}

(a - b)^{2}

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

(a + b)^{3}

(a - b)^{3}

a^{3} + b^{3}

a^{3} - b^{3}

(a + b)^{3} - (a - b)^{3}

(a + b)^{3} - (a - b)^{3} = . . . . . . . . . .

{(a + b)}^{3} - {(a - b)}^{3}

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