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

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

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

simplify

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

a^{3} + b^{3}

Solution steps

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

Expand

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

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

Expand

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

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

Group like terms

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

Add similar elements:

3 a^{2} b - 3 a^{2} b = 0

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

Add similar elements:

3 a b^{2} - 3 a b^{2} = 0

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

(3 y) (- 2 y^{8})

(14)^{2} + (15)^{2} + 20 x

\frac{2}{5 \cdot 125 m ^{4} \cdot n ^{6}}

3 x \cdot 2 y

(0.3 - a) \cdot (0.3 + a)