Expansion of (a + b)ⁿ

(a + b)² = a² + 2ab + b²

(a + b)³ = a³ + 3a²b + 3ab² + b³

(a + b)⁴ = a⁴ + 4a³b + 6a²b² + 4ab³ + b⁴

Note that you are using the numbers in Pascal's triangle.

You can extend this process to find out expansions involving greater powers.

Worked Example

Expand (2x + 3)⁴

Worked Example

Look at relevant expansion of (a + b)

(a + b)⁴ = a⁴ + 4a³b + 6a²b² + 4ab³ + b⁴

Worked Example

Let a = 2x and b = 3, then substitute

= (2x)⁴ + 4(2x)³(3) + 6(2x)²(3)² + 4(2x)(3)³+3⁴

=16x⁴ + 96x³ + 216x² + 81