Find $ \left(x^2+2\right)^3 $ using formula

$$ (A + B) = A^3 + 3A^2B + 3AB^2 + B^3 $$

where $ A = x^2 $ and $ B = 2 $.

$$ \left(x^2+2\right)^3 = \left( x^2 \right)^3+3 \cdot \left( x^2 \right)^2 \cdot 2 + 3 \cdot x^2 \cdot 2^2+2^3 = x^6+6x^4+12x^2+8 $$

Multiply $ \dfrac{1}{8} $ by $ x^6+6x^4+12x^2+8 $ to get $ \dfrac{ x^6+6x^4+12x^2+8 }{ 8 } $.

Step 1: Write $ x^6+6x^4+12x^2+8 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{1}{8} \cdot x^6+6x^4+12x^2+8 & \xlongequal{\text{Step 1}} \frac{1}{8} \cdot \frac{x^6+6x^4+12x^2+8}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 1 \cdot \left( x^6+6x^4+12x^2+8 \right) }{ 8 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ x^6+6x^4+12x^2+8 }{ 8 } \end{aligned} $$