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

The solution to expand (2x-1/2)^3 is (64x^3-48x^2+12x-1)/8

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expand (2x-1/2)^3

expand

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

\frac{64 x ^{3} - 48 x ^{2} + 12 x - 1}{8}

Solution steps

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

Apply Perfect Cube Formula:

(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}

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

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

Simplify

(2 x)^{3} - 3 (2 x)^{2} \frac{1}{2} + 3 \cdot 2 x (\frac{1}{2})^{2} - (\frac{1}{2})^{3} : \frac{64 x ^{3} - 48 x ^{2} + 12 x - 1}{8}

= \frac{64 x ^{3} - 48 x ^{2} + 12 x - 1}{8}

\frac{p - 11}{( p - 1 ) ^{2}}

\frac{2 x + 2}{( x + 2 ) ( x - 2 )}

(1 + x 7)^{2}

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

What is expand (2x-1/2)^3 ?
The solution to expand (2x-1/2)^3 is (64x^3-48x^2+12x-1)/8