Question

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

Answer 1

You can Distribute by rewriting:`(2y + 5x)(2y + 5x)`
which produces: `4y^2+10xy + 10xy + 25x^2`.

Explanation:

Combine the like terms in the "middle" :
`4y^2+20xy+25x^2`

If you want a challenge, you can do this in your head:
1) Square the first term 2y: `2^2y^2`= `4y^2`

2) Take the product of the terms: `2y*5x` = `10xy` and double it!
`2*10xy=20xy`

3) Square the second term: `5^2x^2=25x^2`

4) and combine! `4y^2+20xy+25x^2`

Answer 2

See the entire simplification process below:

Explanation:

First, rewrite this expression as:

`(2y + 5x)(2y + 5x)`

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

`(color(red)(2y) + color(red)(5x))(color(blue)(2y) + color(blue)(5x))` becomes:

`(color(red)(2y) xx color(blue)(2y)) + (color(red)(2y) xx color(blue)(5x)) + (color(red)(5x) xx color(blue)(2y)) + (color(red)(5x) xx color(blue)(5x))`

`4y^2 + 10xy + 10xy + 25x^2`

We can now combine like terms:

`4y^2 + (10 + 10)xy + 25x^2`

`4y^2 + 20xy + 25x^2`