What is expand 0.5*(x^2-4Lx+4L^2)^2 ?

The solution to expand 0.5*(x^2-4Lx+4L^2)^2 is 0.5x^4-4x^3L+12x^2L^2-16xL^3+8L^4

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expand 0.5*(x^2-4Lx+4L^2)^2

expand

0.5 \cdot (x^{2} - 4 Lx + 4 L^{2})^{2}

0.5 x^{4} - 4 x^{3} L + 12 x^{2} L^{2} - 16 x L^{3} + 8 L^{4}

Solution steps

0.5 (x^{2} - 4 Lx + 4 L^{2})^{2}

(x^{2} - 4 Lx + 4 L^{2})^{2} = x^{4} - 8 x^{3} L + 24 x^{2} L^{2} - 32 x L^{3} + 16 L^{4}

= 0.5 (x^{4} - 8 x^{3} L + 24 x^{2} L^{2} - 32 x L^{3} + 16 L^{4})

Distribute parentheses

= 0.5 x^{4} + 0.5 (- 8 x^{3} L) + 0.5 \cdot 24 x^{2} L^{2} + 0.5 (- 32 x L^{3}) + 0.5 \cdot 16 L^{4}

Apply minus-plus rules

+ (- a) = - a

= 0.5 x^{4} - 8 \cdot 0.5 x^{3} L + 24 \cdot 0.5 x^{2} L^{2} - 32 \cdot 0.5 x L^{3} + 16 \cdot 0.5 L^{4}

Simplify

0.5 x^{4} - 8 \cdot 0.5 x^{3} L + 24 \cdot 0.5 x^{2} L^{2} - 32 \cdot 0.5 x L^{3} + 16 \cdot 0.5 L^{4} : 0.5 x^{4} - 4 x^{3} L + 12 x^{2} L^{2} - 16 x L^{3} + 8 L^{4}

= 0.5 x^{4} - 4 x^{3} L + 12 x^{2} L^{2} - 16 x L^{3} + 8 L^{4}

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

(16900 - 260 a + a^{2}) + 360 a - 21600

(1 - x^{2}) x^{''} - 2 x^{'}

\frac{1}{t ( t - 4 )}

\frac{5 π ( 226 226 - 1 )}{27}

What is expand 0.5*(x^2-4Lx+4L^2)^2 ?
The solution to expand 0.5*(x^2-4Lx+4L^2)^2 is 0.5x^4-4x^3L+12x^2L^2-16xL^3+8L^4