What is expand (x^2y^4(6x-1)^2)/4 ?

The solution to expand (x^2y^4(6x-1)^2)/4 is 9x^4y^4-3x^3y^4+(x^2y^4)/4

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expand (x^2y^4(6x-1)^2)/4

expand

\frac{x ^{2} y ^{4} ( 6 x - 1 ) ^{2}}{4}

9 x^{4} y^{4} - 3 x^{3} y^{4} + \frac{x ^{2} y ^{4}}{4}

Solution steps

\frac{x ^{2} y ^{4} ( 6 x - 1 ) ^{2}}{4}

(6 x - 1)^{2} = 36 x^{2} - 12 x + 1

= \frac{x ^{2} y ^{4} ( 36 x ^{2} - 12 x + 1 )}{4}

Expand

x^{2} y^{4} (36 x^{2} - 12 x + 1) : 36 x^{4} y^{4} - 12 x^{3} y^{4} + x^{2} y^{4}

= \frac{36 x ^{4} y ^{4} - 12 x ^{3} y ^{4} + x ^{2} y ^{4}}{4}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{36 x ^{4} y ^{4} - 12 x ^{3} y ^{4} + x ^{2} y ^{4}}{4} = \frac{36 x ^{4} y ^{4}}{4} - \frac{12 x ^{3} y ^{4}}{4} + \frac{x ^{2} y ^{4}}{4}

= \frac{36 x ^{4} y ^{4}}{4} - \frac{12 x ^{3} y ^{4}}{4} + \frac{x ^{2} y ^{4}}{4}

Divide the numbers:

\frac{36}{4} = 9

= 9 x^{4} y^{4} - \frac{12 x ^{3} y ^{4}}{4} + \frac{x ^{2} y ^{4}}{4}

Divide the numbers:

\frac{12}{4} = 3

= 9 x^{4} y^{4} - 3 x^{3} y^{4} + \frac{x ^{2} y ^{4}}{4}

\frac{d}{d θ} ((x (θ)) (a (θ - sin (θ))))

\frac{k ( s + 4 )}{s ( s + 1 ) ( s + 3 )}

(2 - x - 4)^{2}

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

\frac{x - 2}{( x + 2 ) ( x - 4 )}

What is expand (x^2y^4(6x-1)^2)/4 ?
The solution to expand (x^2y^4(6x-1)^2)/4 is 9x^4y^4-3x^3y^4+(x^2y^4)/4