What is factor 9/4 p^2+3/2 pq+1/4 q^2 ?

The solution to factor 9/4 p^2+3/2 pq+1/4 q^2 is ((3p)/2+q/2)^2

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factor 9/4 p^2+3/2 pq+1/4 q^2

factor

\frac{9}{4} p^{2} + \frac{3}{2} pq + \frac{1}{4} q^{2}

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

Solution steps

\frac{9}{4} p^{2} + \frac{3}{2} pq + \frac{1}{4} q^{2}

Rewrite in the form of

a^{2} + 2 ab + b^{2} :

\frac{9 p ^{2}}{4} = (\frac{3}{2} p)^{2}

\frac{q ^{2}}{4} = (\frac{1}{2} q)^{2}

\frac{3 pq}{2} = 2 \cdot \frac{3}{2} p \frac{1}{2} q

= (\frac{3}{2} p)^{2} + 2 \cdot \frac{3}{2} p \frac{1}{2} q + (\frac{1}{2} q)^{2}

Apply Perfect Square Formula:

a^{2} + 2 ab + b^{2} = (a + b)^{2}

(\frac{3}{2} p)^{2} + 2 \cdot \frac{3}{2} p \frac{1}{2} q + (\frac{1}{2} q)^{2} = (\frac{3}{2} p + \frac{1}{2} q)^{2}

= (\frac{3}{2} p + \frac{1}{2} q)^{2}

\frac{2}{11}

\frac{a - 6}{3} > a + 2

(\frac{81 y ^{16}}{16 x ^{12}})^{\frac{1}{4}}

1 + 4

3.5 = - 16 t^{2} + 16 t

What is factor 9/4 p^2+3/2 pq+1/4 q^2 ?
The solution to factor 9/4 p^2+3/2 pq+1/4 q^2 is ((3p)/2+q/2)^2