What is (p-2/q)(p^2+(2p)/q+4/(q^2)) ?

The solution to (p-2/q)(p^2+(2p)/q+4/(q^2)) is ((pq-2)(p^2q^2+2pq+4))/(q^3)

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simplify (p-2/q)(p^2+(2p)/q+4/(q^2))

simplify

(p - \frac{2}{q}) (p^{2} + \frac{2 p}{q} + \frac{4}{q ^{2}})

\frac{( pq - 2 ) ( p ^{2} q ^{2} + 2 pq + 4 )}{q ^{3}}

Solution steps

(p - \frac{2}{q}) (p^{2} + \frac{2 p}{q} + \frac{4}{q ^{2}})

Join

p - \frac{2}{q} : \frac{pq - 2}{q}

= \frac{pq - 2}{q} (p^{2} + \frac{2 p}{q} + \frac{4}{q ^{2}})

Apply the fraction rule:

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

= \frac{( pq - 2 ) ( p ^{2} + \frac{2 p}{q} + \frac{4}{q ^{2}} )}{q}

Simplify

(pq - 2) (p^{2} + \frac{2 p}{q} + \frac{4}{q ^{2}}) : \frac{( pq - 2 ) ( p ^{2} q ^{2} + 2 pq + 4 )}{q ^{2}}

= \frac{\frac{( pq - 2 ) ( p ^{2} q ^{2} + 2 pq + 4 )}{q ^{2}}}{q}

Apply the fraction rule:

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

= \frac{( pq - 2 ) ( p ^{2} q ^{2} + 2 pq + 4 )}{q ^{2} q}

Simplify

q^{2} q : q^{3}

= \frac{( pq - 2 ) ( p ^{2} q ^{2} + 2 pq + 4 )}{q ^{3}}

(a + \frac{1}{6}) (a + \frac{7}{6})

o f (o, x, y) (2 x^{2} - x y - 2 y^{2} = - 4)

2 (- 2 k^{3} + 2 k + k^{2} - k^{4} + \frac{- 8 k + 5 k ^{4} + 8 k ^{3}}{6})

(x + 6) l e f t (x - 6)

5 (x + Δ x)

What is (p-2/q)(p^2+(2p)/q+4/(q^2)) ?
The solution to (p-2/q)(p^2+(2p)/q+4/(q^2)) is ((pq-2)(p^2q^2+2pq+4))/(q^3)