Question

What is the binomial expansion of (m + 2)4?

Answer 1

Answer: x^4 + 8x^3 + 24x^2 + 32x + 16

Explanation:

Given is a binomial as

m+2 and we have to raise to power 4.

We know that

(x+a)^n = x^n+nC1 x^{n-1} a+nC2 x^{n-2} a^2+...nCr x^{n-r} a^r+...+a^n

Here substitute n =4, x=m and a =2

We get

(m+2)^4 =m^4+4C2 m^3(2) +4C2 m^2 (2^2)+4C3 m (2)^3 +4C4 (2)^4\\= m^4+8m^3+24m^2+32m+16

Answer 2

The expansion will have 5 terms with coefficients from row 4 of Pascal’s triangle.