What is expand (x+x^2+x^3)^3 ?

The solution to expand (x+x^2+x^3)^3 is x^9+3x^8+6x^7+7x^6+6x^5+3x^4+x^3

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expand (x+x^2+x^3)^3

expand

(x + x^{2} + x^{3})^{3}

x^{9} + 3 x^{8} + 6 x^{7} + 7 x^{6} + 6 x^{5} + 3 x^{4} + x^{3}

Solution steps

(x + x^{2} + x^{3})^{3}

Simplify

(x + x^{2} + x^{3})^{3} : (x + x^{2} + x^{3}) (x + x^{2} + x^{3}) (x + x^{2} + x^{3})

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

Expand

(x + x^{2} + x^{3}) (x + x^{2} + x^{3}) : x^{6} + 2 x^{5} + 3 x^{4} + 2 x^{3} + x^{2}

= (x^{6} + 2 x^{5} + 3 x^{4} + 2 x^{3} + x^{2}) (x + x^{2} + x^{3})

Distribute parentheses

= x^{6} x + x^{6} x^{2} + x^{6} x^{3} + 2 x^{5} x + 2 x^{5} x^{2} + 2 x^{5} x^{3} + 3 x^{4} x + 3 x^{4} x^{2} + 3 x^{4} x^{3} + 2 x^{3} x + 2 x^{3} x^{2} + 2 x^{3} x^{3} + x^{2} x + x^{2} x^{2} + x^{2} x^{3}

Simplify

x^{6} x + x^{6} x^{2} + x^{6} x^{3} + 2 x^{5} x + 2 x^{5} x^{2} + 2 x^{5} x^{3} + 3 x^{4} x + 3 x^{4} x^{2} + 3 x^{4} x^{3} + 2 x^{3} x + 2 x^{3} x^{2} + 2 x^{3} x^{3} + x^{2} x + x^{2} x^{2} + x^{2} x^{3} : x^{9} + 3 x^{8} + 6 x^{7} + 7 x^{6} + 6 x^{5} + 3 x^{4} + x^{3}

= x^{9} + 3 x^{8} + 6 x^{7} + 7 x^{6} + 6 x^{5} + 3 x^{4} + x^{3}

\frac{v}{( x ^{2} \cdot y ^{3} )} + \frac{u}{x} - w

12 x^{4} + 24 x^{3} y - 36 x^{2} y^{2}

(3 a + 4 a)^{2} + (3 a - 4 a)^{2}

x^{4} - 4 x^{3} - 21 x^{2}

4 lo g_{4} (5) + 5 lo g_{4} (x)

What is expand (x+x^2+x^3)^3 ?
The solution to expand (x+x^2+x^3)^3 is x^9+3x^8+6x^7+7x^6+6x^5+3x^4+x^3