Question

How do you find the product of `(8x + 5) (2x + 9)`?

Answer 1

`16x^2+82x+45`

Explanation:

We must ensure that each term in the 2nd bracket is multiplied by each term in the first bracket. This can be achieved as follows.

`color(red)((8x+5))(2x+9)=color(red)(8x)(2x+9)color(red)(+5)(2x+9)`

distribute the brackets.

`=16x^2+72x+10x+45`

collecting 'like terms' gives: `16x^2+82x+45`

`rArr(8x+5)(2x+9)=16x^2+82x+45`
`color(blue)"-------------------------------------------------------"`

There is another method referred to as FOIL, where

F- the First term in each bracket (multiply together)

O- the Outer term in each bracket (multiply together)

I - the Inner term in each bracket (multiply together)

L - the Last term in each bracket (multiply together)

`rArr(8x+5)(2x+9)`

`=(8x xx2x)+(9xx8x)+(5xx2x)+(5xx9)`

`=16x^2+72x+10x+45=16x^2+82x+45`