Simplify the following expressions- a2 - b2-a - b - a3 - b3-a2 - b2

The given expressions can be written as #160; a^2 b^2a b a^3 b^3a^2 b^2 =(a^2 b^2 )(a+b) (a^3 b^3)(1)a^2 b^2 =(a+b)^2(a b) (a b)(a^2+b^2+ ...

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Addition and Subtraction of Algebraic Expressions

Simplify the ...

Question

Simplify the following expressions.
$\frac{a^{2} - b^{2}}{a - b} - \frac{a^{3} - b^{3}}{a^{2} - b^{2}}$

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Solution

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\frac{(a^{2} - b^{2}) + {(b^{2} - c^{2})}^{3} + {(c^{2} - a^{2})}^{3}}{{(a - b)}^{3} + {(b - c)}^{3} + {(c - a)}^{3}}

(a + b)^{2}

(a - b)^{2}

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

(a + b)^{3}

(a - b)^{3}

a^{3} + b^{3}

a^{3} - b^{3}

(\frac{a^{3} - b^{3}}{a^{2} + b^{2} + a b})

\frac{(a^{2} - b^{2})^{3} + (b^{2} - c^{2})^{3} + (c^{2} - a^{2})^{3}}{(a - b)^{3} + (b - c)^{3} + (c - a)^{3}}

(\frac{a + 3 b}{(a - b)^{2}} + \frac{a - 3 b}{a^{2} - b^{2}}) : \frac{a^{2} + 3 b^{2}}{(a - b)^{2}}

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