What is (1/2 x^3+6x)^2 ?

The solution to (1/2 x^3+6x)^2 is (x^6)/4+6x^4+36x^2

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simplify (1/2 x^3+6x)^2

simplify

(\frac{1}{2} x^{3} + 6 x)^{2}

\frac{x ^{6}}{4} + 6 x^{4} + 36 x^{2}

Solution steps

(\frac{1}{2} x^{3} + 6 x)^{2}

\frac{1}{2} x^{3} = \frac{x ^{3}}{2}

= (\frac{x ^{3}}{2} + 6 x)^{2}

Apply Perfect Square Formula:

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

a = \frac{x ^{3}}{2}, b = 6 x

= (\frac{x ^{3}}{2})^{2} + 2 \cdot \frac{x ^{3}}{2} \cdot 6 x + (6 x)^{2}

Simplify

(\frac{x ^{3}}{2})^{2} + 2 \cdot \frac{x ^{3}}{2} \cdot 6 x + (6 x)^{2} : \frac{x ^{6}}{4} + 6 x^{4} + 36 x^{2}

= \frac{x ^{6}}{4} + 6 x^{4} + 36 x^{2}

3 x y - 6 x + 2 y - 4

\frac{3}{x - 2} + \frac{5}{2 - x}

(\frac{3 m}{4} - 3) + 9

- (- 9 q + 3 r) + 6 r - 2 (- 4 r + 9 q)

(4 x - 3 y)^{5}