Question

How do you expand `(5x+4y)^2`?

Answer 1

`25x^2+40xy+16y^2`

Explanation:

We can write `(5x+4y)^2=(5x+4y)(5x+4y)`

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

`(color(red)(5x+4y))(5x+4y)`

`=color(red)(5x)(5x+4y)color(red)(+4y)(5x+4y)`

now distribute the brackets.

`=25x^2+20xy+20xy+16y^2`

collect like terms.

`25x^2+(20xy+20xy)+16y^2`

`=25x^2+40xy+16y^2`