Question

Expand (x – 4)^5 using the Binomial Theorem and Pascal’s triangle. Show all necessary steps.

Answer 1

SOLUTION

The given expression is:

$(x-4)^5$

Using binomial theorem, the function is expanded as follows:

$(x-4)^5=x^5+5(x)^4(-4)^+\frac{5(5-1)}{2!}x^3(-4)^2+\frac{5(5-1)(5-2)}{3!}x^2(-4)^3+\frac{5(5-1)(5-2)(5-3)}{4!}x^(-4)^4+(-4)^5$

This gives:

$(x-4)^5=x^5-20x^4+160x^3-640x^2+1280x-1024$

The pascal triangle is shown:

Using pascal triangle the expansion is shown:

$\begin{gathered} (x-4)^5=x^5+5x^4(-4)+10x^3(-4)^2+10x^2(-4)^3+5x(-4)^4+(-4)^5 \\ (x-4)^5=x^5-20x^4+160x^3-640x^2+1280x-1024 \end{gathered}$