How do I expand (x+a)(x+b)? (plus example)

The key to understanding expanding brackets is to understand that we need to multipy EVERYTHING in the first bracket by EVERYTHING in the second bracket.

We can think of the calculation

(x+a)(x+b)

as

x(x+b) + a(x+b)

(by simply splitting up the first bracket).

Multiplying out both brackets then gives

xx + xb + ax + ab,

which is equal to 

x² + ax + bx + ab, which is our final answer.

 

 

Example: Expand (x+3)(x+4).

We can think of this as

x(x+4) + 3(x+4),

which we can see is equal to

xx + 4x + 3x + 12,

so our final answer is

x² + 7x + 12.