Question

Use the binomial theorem to expand the binomial.(x – 3)^5

Answer 1

Given:

`(x-3)^5`

To find the binomial expansion.

Formula for the binomial expansion:

`(x+y)^n=nC_0x^n+nC_1x^(n-1)y+nC_2x^(n-2)y^2+\cdots+nC^{}_ny^n`

By substiting the values in the given formula:

`\begin{gathered} (*-3)^5=5C_0x^5+5C_1x^4(-3)+5C_2x^3(-3)^2+5C_3x^2(-3)^3 \\ \text{ }+5C_4x^{}(-3)^4+5C_5(-3)^5 \\ (*-3)^5=x^5-15x^4+90x^3-270x^2+405x-243 \end{gathered}`