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)4 ⇒4C 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
