What are the coefficients for the binomial expansion of (a + b)³?

Solution:

Given expression is

(a + b)³

We know that binomial expansion formula is (x + y)ⁿ = ⁿC\(_0\) xⁿ y⁰ + ⁿC\(_1\) x^{n - 1} y¹ + ⁿC\(_2\) x^n-2 y² + ⁿC\(_3\) x^{n - 3} y³ + ... + ⁿC\(_{n-1}\) x y^{n - 1} + ⁿC\(_n\) x⁰yⁿ

The exponents of the first term keep decreasing and that of the second term keep increasing. The coefficients f the terms after expansion are equidistant from the beginning and the end.

(a + b)³ = a³ + 3a²b + 3ab² + b³

Therefore, the coefficients are 1, 3, 3, 1 respectively.

What are the coefficients for the binomial expansion of (a + b)³?

Summary:

The coefficients of the terms for the binomial expansion of (a + b)³ are 1, 3, 3, 1 respectively.