Question

Use the formula to expand:

(7) ${\left(5x+\frac{1}{2}\right)}^3$

Answer 1

We know that (a + b )³ = a³ + 3a²b + 3ab² + b³
Comparing ${\left(5x+\frac{1}{2}\right)}^3$ with (a + b)³, we get:
a = 5x and b = $\frac{1}{2}$
Substituting these in the above formula:
$$\begin{gathered} {\left(5x+\frac{1}{2}\right)}^3={\left(5x\right)}^3+3\times {\left(5x\right)}^2\times \frac{1}{2}+3\times 5x\times {\left(\frac{1}{2}\right)}^2+{\left(\frac{1}{2}\right)}^3 \\ =125x^3+\frac{75x^2}{2}+\frac{15x}{4}+\frac{1}{8} \end{gathered}$$