Question

How do you simplify the expression `(5x-2)^2`?

Answer 1

`25x^2-20x+4`

Explanation:

To solve this problem first you rewrite as follows:

`(color(blue)(5x)color(darkred)(-2))(color(red)(5x)color(green)(-2))`

Then you proceed to FOIL it:

Where you multiply the `color(blue)"first term"` with the `color(red)"outer term"` then you multiply the `color(blue)"first term"` with the `color(green)"inner term"`:

`(color(blue)(5x))(color(red)(5x))=25x^2`

`(color(blue)(5x))(color(green)(-2))=-10x`

Now you multiply the `color(darkred)"last term"` with the `color(red)"outer term"` then you multiply the `color(darkred)"last term"` with the `color(green)"inner term"`:

`color(darkred)((-2))(color(red)(5x))=-10x`

`color(darkred)((-2))(color(green)(-2))=4`

Now combine them:

`25x^2-10x-10x+4`

Simplify:

`25x^2-20x+4`

Answer 2

`25x^2-20x+4`

Explanation:

`"express " (5x-2)^2" as " (5x-2)(5x-2)`

`"each term in the second bracket is multiplied by each term in"`
`"the first bracket"`

`(color(red)(5x-2))(5x-2)`

`=color(red)(5x)(5x-2)color(red)(-2)(5x-2)`

`=(color(red)(5x)xx5x)+(color(red)(5x)xx-2)+(color(red)(-2)xx5x)+(color(red)(-2)xx-2)`

`=25x^2+(-10x)+(-10x)+4`

`=25x^2-10x-10x+4`

`=25x^2-20x+4`