What is expand (1/4 x-2y^3)^2 ?

The solution to expand (1/4 x-2y^3)^2 is (x^2-16xy^3+64y^6)/(16)

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expand (1/4 x-2y^3)^2

expand

(\frac{1}{4} x - 2 y^{3})^{2}

\frac{x ^{2} - 16 x y ^{3} + 64 y ^{6}}{16}

Solution steps

(\frac{1}{4} x - 2 y^{3})^{2}

Apply Perfect Square Formula:

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

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

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

Simplify

(\frac{1}{4} x)^{2} - 2 \cdot \frac{1}{4} x \cdot 2 y^{3} + (2 y^{3})^{2} : \frac{x ^{2} - 16 x y ^{3} + 64 y ^{6}}{16}

= \frac{x ^{2} - 16 x y ^{3} + 64 y ^{6}}{16}

(e^{8 x} + e^{- 8 x})^{2}

40 (e^{- 2 x} - 2 e^{- 2 x} x)

(3 arctan (x) - π) (x^{2} - 3)

\frac{( n + 1 ) ( n + 2 ) ( n + 3 ) ( n + 4 )}{4}

\frac{125 ( 2 n + 1 ) ( n + 1 )}{6}

What is expand (1/4 x-2y^3)^2 ?
The solution to expand (1/4 x-2y^3)^2 is (x^2-16xy^3+64y^6)/(16)