Factoring Over Multivariable Polynomials Calculator GCF of Polynomial Calculator Factor out the GCF from the Polynomial Calculator Determining if Polynomial is Prime LCM of Polynomials Using GCF Factoring Binomials as sum or difference of cubes Factoring Difference Square Polynomial Calculator Polynomial Root Calculator Factoring Over Complex Numbers Polynomial Equation Solver Calculator

Finding Binomial Expansion of $(1-x^2)^2$

Utilize the Binomial Expansion Calculator and enter your input term in the input field ie., $(1-x^2)^2$ & press the calculate button to get the result ie., $x^4 - 2x^2 + 1$ 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 $(1-x^2)^2$ Using Binomial Theorem

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

So $(1 - x^2)^2$ = $\sum_{k=0}^2 {^2C_k}((1)^{2-k}(-x^2)^{k})$

By expanding the summation:


$= \frac{2}{(2)1}(1)^{2-0}\times{}(-x^2)^0+\frac{2}{(1)1}(1)^{2-1}\times{}(-x^2)^1+\frac{2}{(1)2}(1)^{2-2}\times{}(-x^2)^2$

$= 1(1)^{2-0}\times{}(-x^2)^0+2(1)^{2-1}\times{}(-x^2)^1+1(1)^{2-2}\times{}(-x^2)^2$

$= (1)^{2-0}\times{}(-x^2)^0+(2)(1)^{2-1}\times{}(-x^2)^1+(1)^{2-2}\times{}(-x^2)^2$

$= (1)^{2}\times{}(-x^2)^0+(2)(1)^{1}\times{}(-x^2)^1+(1)^{0}\times{}(-x^2)^2$

$= (1)^{2}\times{}1+(2)(1)^{1}\times{}(-x^2)^1+1\times{}(-x^2)^2$

$= 1\times{}(1)+(2)1\times{}(-x^2)+1\times{}(x^4)$

$= x^4 - 2x^2 + 1$

FAQs on Binomial Expansion of $(1-x^2)^2$

1. How to simplify the Binomial Expansion $(1-x^2)^2$?

You can expand the given term $(1-x^2)^2$ in a binomial expansion by using Newton's binomial theorem & the formula of it.

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

The Binomial Expansion of $(1-x^2)^2$ is $x^4 - 2x^2 + 1$.

3. Where can I obtain a step by step solution to expand the given binomial $(1-x^2)^2$?

You can obtain the step by step solution for Binomial Expansion of $(1-x^2)^2$ on our page.