What is (3/4 x^2y^2+5/2 a^2)^2 ?

The solution to (3/4 x^2y^2+5/2 a^2)^2 is (9x^4y^4}{16}+\frac{15a^2x^2y^2+25a^4)/4

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simplify (3/4 x^2y^2+5/2 a^2)^2

simplify

(\frac{3}{4} x^{2} y^{2} + \frac{5}{2} a^{2})^{2}

\frac{9 x ^{4} y ^{4}}{16} + \frac{15 a ^{2} x ^{2} y ^{2} + 25 a ^{4}}{4}

Solution steps

(\frac{3}{4} x^{2} y^{2} + \frac{5}{2} a^{2})^{2}

Multiply

\frac{3}{4} x^{2} y^{2} : \frac{3 x ^{2} y ^{2}}{4}

= (\frac{3 x ^{2} y ^{2}}{4} + \frac{5}{2} a^{2})^{2}

Multiply

\frac{5}{2} a^{2} : \frac{5 a ^{2}}{2}

= (\frac{3 x ^{2} y ^{2}}{4} + \frac{5 a ^{2}}{2})^{2}

Apply Perfect Square Formula:

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

a = \frac{3 x ^{2} y ^{2}}{4}, b = \frac{5 a ^{2}}{2}

= (\frac{3 x ^{2} y ^{2}}{4})^{2} + 2 \cdot \frac{3 x ^{2} y ^{2}}{4} \cdot \frac{5 a ^{2}}{2} + (\frac{5 a ^{2}}{2})^{2}

Simplify

(\frac{3 x ^{2} y ^{2}}{4})^{2} + 2 \cdot \frac{3 x ^{2} y ^{2}}{4} \cdot \frac{5 a ^{2}}{2} + (\frac{5 a ^{2}}{2})^{2} : \frac{9 x ^{4} y ^{4}}{16} + \frac{15 a ^{2} x ^{2} y ^{2} + 25 a ^{4}}{4}

= \frac{9 x ^{4} y ^{4}}{16} + \frac{15 a ^{2} x ^{2} y ^{2} + 25 a ^{4}}{4}

\frac{( ( n - 2 ) ! ( n + 2 ) ! )}{( ( n + 3 ) ! ( n - 1 ) ! )}

\frac{2 sin ^{2} ( x )}{sin ^{2} ( x ) + 2 cos ^{2} ( x )}

3 n + 3

7 \times (- 3) + (- 2) \times (- 13)

(\frac{x}{y} + \frac{y}{2} + \frac{z}{x})^{2}

What is (3/4 x^2y^2+5/2 a^2)^2 ?
The solution to (3/4 x^2y^2+5/2 a^2)^2 is (9x^4y^4}{16}+\frac{15a^2x^2y^2+25a^4)/4