How do you use the binomial formula to expand (x+1)3?

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)3

Binomial formula for (a+b)33C 0 a 3 b 0 +3C 1 a 2 b 1 +3C2a 1 b 2 +3C 3 a 0 b 3 + ……..

Expand  (x+1)3

So using the above formula we will expand (x+1)3

Here, a=x and b=1.

3C 0 x 3 +3C 1 x 2 ×1 1 +3C 2 x 1 ×1 2 +3C 3 ×1 3

We know that

3C 0 =3C 3 =1

3C 1 =3C 2 =3

On substituting above value in the above equation we get

x 3 +3x 2 +3x+1

Answer

Expansion of  (x+1)3 is x 3 +3x 2 +3x+1

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