What is ((a+b)(a^3-b^3))/((a^2-b^2)) ?

The solution to ((a+b)(a^3-b^3))/((a^2-b^2)) is a^2+ab+b^2

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simplify ((a+b)(a^3-b^3))/((a^2-b^2))

simplify

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

a^{2} + ab + b^{2}

Solution steps

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

Apply Difference of Two Squares Formula:

x^{2} - y^{2} = (x + y) (x - y)

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

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

Cancel the common factor:

a + b

= \frac{a ^{3} - b ^{3}}{a - b}

Apply Difference of Cubes Formula:

x^{3} - y^{3} = (x - y) (x^{2} + x y + y^{2})

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

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

Cancel the common factor:

a - b

= a^{2} + ab + b^{2}

\frac{( 9 ^{n + 2} + 10 \cdot 9 ^{n} )}{( 9 ^{n + 1} \cdot 11 - 8 \cdot 9 ^{n} )}

x + 3 + x - 3

2 x^{2} + 9 x y + 9 y^{2}

(4 b + 6 y)^{3}

4 \cdot (\frac{1}{y + 1})^{6}

What is ((a+b)(a^3-b^3))/((a^2-b^2)) ?
The solution to ((a+b)(a^3-b^3))/((a^2-b^2)) is a^2+ab+b^2