What is expand (3x^3-2xy+3)^4x ?

The solution to expand (3x^3-2xy+3)^4x is

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expand (3x^3-2xy+3)^4x

expand

(3 x^{3} - 2 x y + 3)^{4} x

81 x^{13} - 216 x^{11} y + 324 x^{10} + 216 x^{9} y^{2} - 648 x^{8} y - 96 x^{7} y^{3} + 486 x^{7} + 432 x^{6} y^{2} + 16 x^{5} y^{4} - 648 x^{5} y - 96 x^{4} y^{3} + 324 x^{4} + 216 x^{3} y^{2} - 216 x^{2} y + 81 x

Solution steps

(3 x^{3} - 2 x y + 3)^{4} x

(3 x^{3} - 2 x y + 3)^{4} = 81 x^{12} - 216 x^{10} y + 324 x^{9} + 216 x^{8} y^{2} - 648 x^{7} y - 96 x^{6} y^{3} + 486 x^{6} + 432 x^{5} y^{2} + 16 x^{4} y^{4} - 648 x^{4} y - 96 x^{3} y^{3} + 324 x^{3} + 216 x^{2} y^{2} - 216 x y + 81

= x (81 x^{12} - 216 x^{10} y + 324 x^{9} + 216 x^{8} y^{2} - 648 x^{7} y + 486 x^{6} - 96 x^{6} y^{3} + 432 x^{5} y^{2} + 16 x^{4} y^{4} - 648 x^{4} y + 324 x^{3} - 96 x^{3} y^{3} + 216 x^{2} y^{2} - 216 x y + 81)

= x (81 x^{12} - 216 x^{10} y + 324 x^{9} + 216 x^{8} y^{2} - 648 x^{7} y - 96 x^{6} y^{3} + 486 x^{6} + 432 x^{5} y^{2} + 16 x^{4} y^{4} - 648 x^{4} y - 96 x^{3} y^{3} + 324 x^{3} + 216 x^{2} y^{2} - 216 x y + 81)

Distribute parentheses

= x \cdot 81 x^{12} + x (- 216 x^{10} y) + x \cdot 324 x^{9} + x \cdot 216 x^{8} y^{2} + x (- 648 x^{7} y) + x (- 96 x^{6} y^{3}) + x \cdot 486 x^{6} + x \cdot 432 x^{5} y^{2} + x \cdot 16 x^{4} y^{4} + x (- 648 x^{4} y) + x (- 96 x^{3} y^{3}) + x \cdot 324 x^{3} + x \cdot 216 x^{2} y^{2} + x (- 216 x y) + x \cdot 81

Apply minus-plus rules

+ (- a) = - a

= 81 x^{12} x - 216 x^{10} x y + 324 x^{9} x + 216 x^{8} x y^{2} - 648 x^{7} x y - 96 x^{6} x y^{3} + 486 x^{6} x + 432 x^{5} x y^{2} + 16 x^{4} x y^{4} - 648 x^{4} x y - 96 x^{3} x y^{3} + 324 x^{3} x + 216 x^{2} x y^{2} - 216 xx y + 81 x

Simplify

81 x^{12} x - 216 x^{10} x y + 324 x^{9} x + 216 x^{8} x y^{2} - 648 x^{7} x y - 96 x^{6} x y^{3} + 486 x^{6} x + 432 x^{5} x y^{2} + 16 x^{4} x y^{4} - 648 x^{4} x y - 96 x^{3} x y^{3} + 324 x^{3} x + 216 x^{2} x y^{2} - 216 xx y + 81 x : 81 x^{13} - 216 x^{11} y + 324 x^{10} + 216 x^{9} y^{2} - 648 x^{8} y - 96 x^{7} y^{3} + 486 x^{7} + 432 x^{6} y^{2} + 16 x^{5} y^{4} - 648 x^{5} y - 96 x^{4} y^{3} + 324 x^{4} + 216 x^{3} y^{2} - 216 x^{2} y + 81 x

= 81 x^{13} - 216 x^{11} y + 324 x^{10} + 216 x^{9} y^{2} - 648 x^{8} y - 96 x^{7} y^{3} + 486 x^{7} + 432 x^{6} y^{2} + 16 x^{5} y^{4} - 648 x^{5} y - 96 x^{4} y^{3} + 324 x^{4} + 216 x^{3} y^{2} - 216 x^{2} y + 81 x

, x (x + 1) (x - 4)

\frac{3 x}{( x + 1 ) ( x + 2 )}

\frac{d ^{2}}{d x ^{2}} ((y) (2 x^{2} + cos (x)))

\frac{8 ( - 3 x ^{2} + 2 )}{( x ^{2} + 2 ) ^{3}}

\frac{( n ( n + 1 ) )}{2}