Expand (x - 1)4?

A binomial expression is an expression containing two terms joined by either addition or subtraction sign. For instance, (x + y) and (2 – x) are examples of binomial expressions.

Binomial Theorem

The Binomial Theorem states the algebraic expansion of exponents of a binomial, which means it is possible to expand a polynomial (a + b)n into the multiple terms. \((a+b)^{n} =\sum_{k=0}^{n}\begin{pmatrix} n\\ k \end{pmatrix}a^{n-k}b^{k}\)

Binomial formula to expand (a+b)4

Binomial formula for (a+b)44C 0 a 4 b 0 +4C 1 a 3 b 1 +4C2a 2 b 2 +4C 4 a 1 b 3 + ……..

Expand (x-1)4

So using the above formula we will expand (x-1)4

Here, a=x and b=-1.

4C 0 x 4 +4C 1 x 4×(-1) 1 +4C 2 x 2 ×(-1) 2 +4C 4 ×(-1) 4+ ……….

We know that 4C 0 =4C 4 =1 4C 1 =4C 2 =4

On substituting above values in the above equation we get

x 4 -4x 3 +6x2 -4x +1

Answer (x-1)4= x 4 -4x 3 +6x2 -4x +1

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