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

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

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

simplify

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

3 a^{2} + b^{2}

Solution steps

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

Apply rule:

(a) = a

(a + b) = a + b

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

Expand

(a + b)^{3} - (a - b)^{3} : 6 a^{2} b + 2 b^{3}

= \frac{6 a ^{2} b + 2 b ^{3}}{a + b - ( a - b )}

Simplify

a + b - (a - b) : 2 b

= \frac{6 a ^{2} b + 2 b ^{3}}{2 b}

Factor

6 a^{2} b + 2 b^{3} : 2 b (3 a^{2} + b^{2})

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

Cancel the common factor:

2

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

Cancel the common factor:

b

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

3 x 1 0^{8}

9 i^{2}

(5 a + 3 b)^{2}

\frac{3}{3 + 1}

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