Question

How do you simplify ${(x-3)}^3$?

Answer 1

Solve for the simplified form

${(x-3)}^3$ can be solved using the identity

${(a–b)}^3=a^3–b^3–3ab(a–b)$

Here we have, $a=x,b=3$ Substituting the values we get

$$\begin{gathered} \Rightarrow {(x-3)}^3=x^3–3^3–3\times x\times 3(x-3) \\ \Rightarrow {(x-3)}^3=x^3–3^3–9x(x-3) \\ \Rightarrow {(x-3)}^3=x^3–3^3–9x^2+27x \end{gathered}$$

Hence, the required answer is ${(x-3)}^3$ is $x^3–9x^2+27x-27$