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

The solution to expand (1/2 x^3+6x)^2 is (x^6+24x^4+144x^2)/4

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

expand

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

\frac{x ^{6} + 24 x ^{4} + 144 x ^{2}}{4}

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

(\frac{1}{2} x^{3})^{2} + 2 \cdot \frac{1}{2} x^{3} \cdot 6 x + (6 x)^{2} : \frac{x ^{6} + 24 x ^{4} + 144 x ^{2}}{4}

= \frac{x ^{6} + 24 x ^{4} + 144 x ^{2}}{4}

(5 x + 2) (5 x - 2)

\frac{5}{( x + 5 ) ^{2}}

3 (ln (x) + 1)

x^{2} e^{x} - 2 (e^{x} x - e^{x})

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

What is expand (1/2 x^3+6x)^2 ?
The solution to expand (1/2 x^3+6x)^2 is (x^6+24x^4+144x^2)/4