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

The solution to expand (4x^2-2y^3)^4 is 256x^8-512x^6y^3+384x^4y^6-128x^2y^9+16y^{12}

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

expand

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

256 x^{8} - 512 x^{6} y^{3} + 384 x^{4} y^{6} - 128 x^{2} y^{9} + 16 y^{12}

Solution steps

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

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

Expand summation

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

Simplify

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

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (4 x^{2})^{3} (- 2 y^{3})^{1} : - 512 x^{6} y^{3}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (4 x^{2})^{2} (- 2 y^{3})^{2} : 384 x^{4} y^{6}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (4 x^{2})^{1} (- 2 y^{3})^{3} : - 128 x^{2} y^{9}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (4 x^{2})^{0} (- 2 y^{3})^{4} : 16 y^{12}

= 256 x^{8} - 512 x^{6} y^{3} + 384 x^{4} y^{6} - 128 x^{2} y^{9} + 16 y^{12}

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

\frac{81}{4}

(5^{3})^{6}

(Q + 6) (3 Q + 5)

lo g_{10} (32)

What is expand (4x^2-2y^3)^4 ?
The solution to expand (4x^2-2y^3)^4 is 256x^8-512x^6y^3+384x^4y^6-128x^2y^9+16y^{12}