Finding Binomial Expansion of $(1-3x)^7$

Utilize the Binomial Expansion Calculator and enter your input term in the input field ie., $(1-3x)^7$ & press the calculate button to get the result ie., $-2187x^7 + 5103x^6 - 5103x^5 + 2835x^4 - 945x^3 + 189x^2 - 21x + 1$ along with a detailed solution in a fraction of seconds.

Ex: (x+1)^2 (or) (x+7)^7 (or) (x+3)^4

Binomial Expansion of:

Elaborate Steps to Expand $(1-3x)^7$ Using Binomial Theorem

According to the binomial formula $(a+b)^n$ = $\sum_{k=0}^{n} {^nC_k}(a^{n-k}b^{k})$

So $(1 - 3.x)^7$ = $\sum_{k=0}^7 {^7C_k}((1)^{7-k}(-3.x)^{k})$

By expanding the summation:

$\frac{7!}{(7-0)!0!}(1)^{7-0}\times{}(-3.x)^0+\frac{7!}{(7-1)!1!}(1)^{7-1}\times{}(-3.x)^1+\frac{7!}{(7-2)!2!}(1)^{7-2}\times{}(-3.x)^2+\frac{7!}{(7-3)!3!}(1)^{7-3}\times{}(-3.x)^3+\frac{7!}{(7-4)!4!}(1)^{7-4}\times{}(-3.x)^4+\frac{7!}{(7-5)!5!}(1)^{7-5}\times{}(-3.x)^5+\frac{7!}{(7-6)!6!}(1)^{7-6}\times{}(-3.x)^6+\frac{7!}{(7-7)!7!}(1)^{7-7}\times{}(-3.x)^7$

$= \frac{5040}{(5040)1}(1)^{7-0}\times{}(-3.x)^0+\frac{5040}{(720)1}(1)^{7-1}\times{}(-3.x)^1+\frac{5040}{(120)2}(1)^{7-2}\times{}(-3.x)^2+\frac{5040}{(24)6}(1)^{7-3}\times{}(-3.x)^3+\frac{5040}{(6)24}(1)^{7-4}\times{}(-3.x)^4+\frac{5040}{(2)120}(1)^{7-5}\times{}(-3.x)^5+\frac{5040}{(1)720}(1)^{7-6}\times{}(-3.x)^6+\frac{5040}{(1)5040}(1)^{7-7}\times{}(-3.x)^7$

$= 1(1)^{7-0}\times{}(-3.x)^0+7(1)^{7-1}\times{}(-3.x)^1+21(1)^{7-2}\times{}(-3.x)^2+35(1)^{7-3}\times{}(-3.x)^3+35(1)^{7-4}\times{}(-3.x)^4+21(1)^{7-5}\times{}(-3.x)^5+7(1)^{7-6}\times{}(-3.x)^6+1(1)^{7-7}\times{}(-3.x)^7$

$= (1)^{7-0}\times{}(-3.x)^0+(7)(1)^{7-1}\times{}(-3.x)^1+(21)(1)^{7-2}\times{}(-3.x)^2+(35)(1)^{7-3}\times{}(-3.x)^3+(35)(1)^{7-4}\times{}(-3.x)^4+(21)(1)^{7-5}\times{}(-3.x)^5+(7)(1)^{7-6}\times{}(-3.x)^6+(1)^{7-7}\times{}(-3.x)^7$

$= (1)^{7}\times{}(-3.x)^0+(7)(1)^{6}\times{}(-3.x)^1+(21)(1)^{5}\times{}(-3.x)^2+(35)(1)^{4}\times{}(-3.x)^3+(35)(1)^{3}\times{}(-3.x)^4+(21)(1)^{2}\times{}(-3.x)^5+(7)(1)^{1}\times{}(-3.x)^6+(1)^{0}\times{}(-3.x)^7$

$= (1)^{7}\times{}1+(7)(1)^{6}\times{}(-3.x)^1+(21)(1)^{5}\times{}(-3.x)^2+(35)(1)^{4}\times{}(-3.x)^3+(35)(1)^{3}\times{}(-3.x)^4+(21)(1)^{2}\times{}(-3.x)^5+(7)(1)^{1}\times{}(-3.x)^6+1\times{}(-3.x)^7$

$= 1\times{}(1)+(7)1\times{}(-3.x)+(21)1\times{}(9.x^2)+(35)1\times{}(-27.x^3)+(35)1\times{}(81.x^4)+(21)1\times{}(-243.x^5)+(7)1\times{}(729.x^6)+1\times{}(-2187.x^7)$

$= -2187x^7 + 5103x^6 - 5103x^5 + 2835x^4 - 945x^3 + 189x^2 - 21x + 1$

FAQs on Binomial Expansion of $(1-3x)^7$

1. How to simplify the Binomial Expansion $(1-3x)^7$?

You can expand the given term $(1-3x)^7$ in a binomial expansion by using Newton's binomial theorem & the formula of it.

2. What is the Binomial Expansion of $(1-3x)^7$?

The Binomial Expansion of $(1-3x)^7$ is $-2187x^7 + 5103x^6 - 5103x^5 + 2835x^4 - 945x^3 + 189x^2 - 21x + 1$.

3. Where can I obtain a step by step solution to expand the given binomial $(1-3x)^7$?

You can obtain the step by step solution for Binomial Expansion of $(1-3x)^7$ on our page.