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

The solution to expand (4x^2-3y^3)^4 is 256x^8-768x^6y^3+864x^4y^6-432x^2y^9+81y^{12}

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expand (4x^2-3y^3)^4

expand

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

256 x^{8} - 768 x^{6} y^{3} + 864 x^{4} y^{6} - 432 x^{2} y^{9} + 81 y^{12}

Solution steps

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

Apply binomial theorem:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = 4 x^{2}, b = - 3 y^{3}

= i = 0 \sum 4 (i 4) (4 x^{2})^{(4 - i)} (- 3 y^{3})^{i}

Expand summation

= \frac{4 !}{0 ! ( 4 - 0 ) !} (4 x^{2})^{4} (- 3 y^{3})^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} (4 x^{2})^{3} (- 3 y^{3})^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} (4 x^{2})^{2} (- 3 y^{3})^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} (4 x^{2})^{1} (- 3 y^{3})^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} (4 x^{2})^{0} (- 3 y^{3})^{4}

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (4 x^{2})^{4} (- 3 y^{3})^{0} : 256 x^{8}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (4 x^{2})^{3} (- 3 y^{3})^{1} : - 768 x^{6} y^{3}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (4 x^{2})^{2} (- 3 y^{3})^{2} : 864 x^{4} y^{6}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (4 x^{2})^{1} (- 3 y^{3})^{3} : - 432 x^{2} y^{9}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (4 x^{2})^{0} (- 3 y^{3})^{4} : 81 y^{12}

= 256 x^{8} - 768 x^{6} y^{3} + 864 x^{4} y^{6} - 432 x^{2} y^{9} + 81 y^{12}

8 x^{6} + 7 x^{3} - 1

\frac{( x ^{- 2} y ^{4} ) ^{3}}{( x y ) ^{- 3}}

(5 + 24 + 5 - 24)^{2}

192 a^{36} b^{9}

\frac{p ^{2} + p}{2 p}

What is expand (4x^2-3y^3)^4 ?
The solution to expand (4x^2-3y^3)^4 is 256x^8-768x^6y^3+864x^4y^6-432x^2y^9+81y^{12}