Question

Use Pascal’s Triangle to expand the following binomials.(x² - 2)³

Answer 1

`(x^(2)-2)^(3)=x^(6)-6x^(4)+12x^(2)-8`

Explanation:

Pascal's triangle applies to this as follows:

Therefore, we apply for this case:

`\begin{gathered} (a-b)^3=a^3-3a^2b+3ab^2-b^3 \\ \\ a=x^2 \\ \\ b=2 \\ \\ \left(x^2-2\right)^3=\left(x^2\right)^3-3\left(x^2\right)^2\cdot\:2+3x^2\cdot\:2^2-2^3 \\ \\ \left(x^2-2\right)^3=x^(2\cdot\:3)-6\left(x^2\right)^2+3x^2\cdot\:4-8 \\ \\ \left(x^2-2\right)^3=x^6-6x^4+12x^2-8 \end{gathered}`