What is expand ((-10+x^2+y^2)^2)/4 ?

The solution to expand ((-10+x^2+y^2)^2)/4 is (x^2y^2)/2-5x^2+(x^4)/4-5y^2+(y^4)/4+25

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expand ((-10+x^2+y^2)^2)/4

expand

\frac{( - 10 + x ^{2} + y ^{2} ) ^{2}}{4}

\frac{x ^{2} y ^{2}}{2} - 5 x^{2} + \frac{x ^{4}}{4} - 5 y^{2} + \frac{y ^{4}}{4} + 25

Solution steps

\frac{( - 10 + x ^{2} + y ^{2} ) ^{2}}{4}

(- 10 + x^{2} + y^{2})^{2} = 2 x^{2} y^{2} - 20 x^{2} + x^{4} - 20 y^{2} + y^{4} + 100

= \frac{2 x ^{2} y ^{2} - 20 x ^{2} + x ^{4} - 20 y ^{2} + y ^{4} + 100}{4}

Apply the fraction rule:

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

\frac{2 x ^{2} y ^{2} - 20 x ^{2} + x ^{4} - 20 y ^{2} + y ^{4} + 100}{4} = \frac{2 x ^{2} y ^{2}}{4} - \frac{20 x ^{2}}{4} + \frac{x ^{4}}{4} - \frac{20 y ^{2}}{4} + \frac{y ^{4}}{4} + \frac{100}{4}

= \frac{2 x ^{2} y ^{2}}{4} - \frac{20 x ^{2}}{4} + \frac{x ^{4}}{4} - \frac{20 y ^{2}}{4} + \frac{y ^{4}}{4} + \frac{100}{4}

\frac{2 x ^{2} y ^{2}}{4} = \frac{x ^{2} y ^{2}}{2}

\frac{20 x ^{2}}{4} = 5 x^{2}

\frac{20 y ^{2}}{4} = 5 y^{2}

\frac{100}{4} = 25

= \frac{x ^{2} y ^{2}}{2} - 5 x^{2} + \frac{x ^{4}}{4} - 5 y^{2} + \frac{y ^{4}}{4} + 25

\frac{3 + 9 x}{( 1 + x ) ( 3 + 5 x )}

(x - 2 - i) (x - 2 + i)

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

1 + \frac{( e ^{x} - e ^{- x} ) ^{2}}{4}

\frac{d}{d y} ((x) (x - y))

What is expand ((-10+x^2+y^2)^2)/4 ?
The solution to expand ((-10+x^2+y^2)^2)/4 is (x^2y^2)/2-5x^2+(x^4)/4-5y^2+(y^4)/4+25