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:

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