Expanding Products of Binomials

# Expanding Products of Binomials

GCSE(F) GCSE(H)

Expressions can contain more than one set of brackets: (x + 3)(x + 2). In this instance, each of the terms in the first bracket must be multiplied by each of the terms in the second bracket. There are various methods for ensuring that this is completed (such as FOIL and FACE); one of the simpler ways is to use a grid:

 x +3 x +2

placing the (in this instance) x + 3 in the top row and the x + 2 as the column entries.

Next, carry out the multiplication of each term:

 x +3 x x2 +3x +2 +2x +6

and finally add the terms together: x2 + 3x + 2x + 6;

then collect the like terms: x2 + 5x + 6.

## Examples

1. Expand and simplify: (2x - 3)(5x + 7).

Answer: 10x2 - x - 21

 2x -3 5x 10x2 -15x +7 14x -21

10x2 -15x + 14x -21 = 10x2 - x + 21

2. Expand and simplify: (ab + 3)(4b + 2).

Answer: 4ab2 + 12b + 2ab + 6

 ab +3 4b 4ab2 +12b +2 +2ab +6

4ab2 +12b + 2ab +6; the expression cannot be simplified any further.