What is expand ((15p+4q)^2)/(400) ?

The solution to expand ((15p+4q)^2)/(400) is (9p^2)/(16)+(3pq)/(10)+(q^2)/(25)

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expand ((15p+4q)^2)/(400)

expand

\frac{( 15 p + 4 q ) ^{2}}{400}

\frac{9 p ^{2}}{16} + \frac{3 pq}{10} + \frac{q ^{2}}{25}

Solution steps

\frac{( 15 p + 4 q ) ^{2}}{400}

(15 p + 4 q)^{2} = 225 p^{2} + 120 pq + 16 q^{2}

= \frac{225 p ^{2} + 120 pq + 16 q ^{2}}{400}

Apply the fraction rule:

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

\frac{225 p ^{2} + 120 pq + 16 q ^{2}}{400} = \frac{225 p ^{2}}{400} + \frac{120 pq}{400} + \frac{16 q ^{2}}{400}

= \frac{225 p ^{2}}{400} + \frac{120 pq}{400} + \frac{16 q ^{2}}{400}

Cancel

\frac{225 p ^{2}}{400} : \frac{9 p ^{2}}{16}

= \frac{9 p ^{2}}{16} + \frac{120 pq}{400} + \frac{16 q ^{2}}{400}

Cancel

\frac{120 pq}{400} : \frac{3 pq}{10}

= \frac{9 p ^{2}}{16} + \frac{3 pq}{10} + \frac{16 q ^{2}}{400}

Cancel

\frac{16 q ^{2}}{400} : \frac{q ^{2}}{25}

= \frac{9 p ^{2}}{16} + \frac{3 pq}{10} + \frac{q ^{2}}{25}

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What is expand ((15p+4q)^2)/(400) ?
The solution to expand ((15p+4q)^2)/(400) is (9p^2)/(16)+(3pq)/(10)+(q^2)/(25)