Simplify a3 - b3a2 - b2 - ab is equal to

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Algebraic Identities

Simplify a3...

Question

Simplify $(\frac{a^{3} - b^{3}}{a^{2} + b^{2} + a b})$ is equal to

a - b

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a + b

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a^{2} - b^{2}

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1

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Solution

The correct option is A $a - b$
We know that one of the algebraic formula is $a^{3} - b^{3} = (a - b) (a^{2} + b^{2} + a b)$ , therefore, we solve the given expression

$= \frac{a^{3} - b^{3}}{a^{2} + b^{2} + a b}$ using the above formula as shown below:

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

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

Hence, $\frac{a^{3} - b^{3}}{a^{2} + b^{2} + a b} = a - b$ .

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Simplify (a3−b3a2+b2+ab) is equal to

The correct option is A a−bWe know that one of the algebraic formula is a3−b3=(a−b)(a2+b2+ab), therefore, we solve the given expression =a3−b3a2+b2+ab using the above formula as shown below:=a3−b3a2+b2+ab=(a−b)(a2+b2+ab)a2+b2+ab=a−bHence, a3−b3a2+b2+ab=a−b.

Simplify $(\frac{a^{3} - b^{3}}{a^{2} + b^{2} + a b})$ is equal to