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

Solution:

The binomial theorem or binomial expansion expresses the algebraic expansion of powers of a binomial.

Here's is a comprehensive expansion to this binomial expression.

(x + y) a = ∑ab=0 (a / b)  xa-b yb

So, binomial expansion formula for (a+b)3 is 

⇒ 3C0 a3 × b0 + 3C1 a2 × b1 + 3C2 a1 × b2 + 3C3 a0 × b3

By 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 x1 ×  (1)2 + 3C 3 × (1)3

By substituting above values in the equation, we get

∵ 3C 0 = 3C 3 = 1 and 3C 1 = 3C 2 = 3

⇒ 1 × x3 + 3 × x2 × (1) + 3 ×  x ×  (1)2 + 1 × (1)3 

⇒ x 3 + 3x 2 + 3x + 1                                            

Thus, the value of (x + 1)3 is x3 + 3x2 + 3x + 1

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

The value of (x + 1)3  = x 3 + 3x2 + 3x + 1

Math worksheets and
visual curriculum