What is expand (((q-p))/2)^2+q*p ?

The solution to expand (((q-p))/2)^2+q*p is (q^2)/4+(qp)/2+(p^2)/4

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expand (((q-p))/2)^2+q*p

expand

(\frac{( q - p )}{2})^{2} + q \cdot p

\frac{q ^{2}}{4} + \frac{qp}{2} + \frac{p ^{2}}{4}

Solution steps

(\frac{q - p}{2})^{2} + qp

(\frac{q - p}{2})^{2} = \frac{q ^{2} - 2 qp + p ^{2}}{2 ^{2}}

= \frac{q ^{2} - 2 qp + p ^{2}}{2 ^{2}} + qp

Convert element to fraction:

qp = \frac{qp 2 ^{2}}{2 ^{2}}

= \frac{q ^{2} - 2 qp + p ^{2}}{2 ^{2}} + \frac{qp \cdot 2 ^{2}}{2 ^{2}}

Since the denominators are equal, combine the fractions:

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

= \frac{q ^{2} - 2 qp + p ^{2} + qp \cdot 2 ^{2}}{2 ^{2}}

q^{2} - 2 qp + p^{2} + qp \cdot 2^{2} = q^{2} + 2 qp + p^{2}

= \frac{q ^{2} + 2 qp + p ^{2}}{2 ^{2}}

2^{2} = 4

= \frac{q ^{2} + 2 qp + p ^{2}}{4}

Apply the fraction rule:

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

\frac{q ^{2} + 2 qp + p ^{2}}{4} = \frac{q ^{2}}{4} + \frac{2 qp}{4} + \frac{p ^{2}}{4}

= \frac{q ^{2}}{4} + \frac{2 qp}{4} + \frac{p ^{2}}{4}

Cancel

\frac{2 qp}{4} : \frac{qp}{2}

= \frac{q ^{2}}{4} + \frac{qp}{2} + \frac{p ^{2}}{4}

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

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What is expand (((q-p))/2)^2+q*p ?
The solution to expand (((q-p))/2)^2+q*p is (q^2)/4+(qp)/2+(p^2)/4