What is expand sqrt(x)(ax-x)^2dx ?

The solution to expand sqrt(x)(ax-x)^2dx is a^2x^2sqrt(x)dx-2ax^2sqrt(x)dx+x^2sqrt(x)dx

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expand sqrt(x)(ax-x)^2dx

expand

x (a x - x)^{2} d x

a^{2} x^{2} x d x - 2 a x^{2} x d x + x^{2} x d x

Solution steps

x (a x - x)^{2} d x

(a x - x)^{2} = a^{2} x^{2} - 2 a x^{2} + x^{2}

= x (a^{2} x^{2} + x^{2} - 2 a x^{2}) d x

Distribute parentheses

= x d x a^{2} x^{2} + x d x (- 2 a x^{2}) + x d x x^{2}

Apply minus-plus rules

+ (- a) = - a

= a^{2} x^{2} x d x - 2 a x^{2} x d x + x^{2} x d x

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

(x - 13 - x)^{2}

(5 x^{2} - y^{3}) d e (- 3 y^{3} + 8 x^{2})

(x + 6 y = 1, 1) (5 x - 15 y = 10)

sin (3 (t - 7))

What is expand sqrt(x)(ax-x)^2dx ?
The solution to expand sqrt(x)(ax-x)^2dx is a^2x^2sqrt(x)dx-2ax^2sqrt(x)dx+x^2sqrt(x)dx