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

2 Answers
Jan 21, 2017

You can Distribute by rewriting: (2y + 5x)(2y + 5x)(2y+5x)(2y+5x)
which produces: 4y^2+10xy + 10xy + 25x^24y2+10xy+10xy+25x2.

Explanation:

Combine the like terms in the "middle" :
4y^2+20xy+25x^24y2+20xy+25x2

If you want a challenge, you can do this in your head:
1) Square the first term 2y: 2^2y^222y2= 4y^24y2

2) Take the product of the terms: 2y*5x2y5x = 10xy10xy and double it!
2*10xy=20xy210xy=20xy

3) Square the second term: 5^2x^2=25x^252x2=25x2

4) and combine! 4y^2+20xy+25x^24y2+20xy+25x2

Jan 21, 2017

See the entire simplification process below:

Explanation:

First, rewrite this expression as:

(2y + 5x)(2y + 5x)(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))(2y+5x)(2y+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))(2y×2y)+(2y×5x)+(5x×2y)+(5x×5x)

4y^2 + 10xy + 10xy + 25x^24y2+10xy+10xy+25x2

We can now combine like terms:

4y^2 + (10 + 10)xy + 25x^24y2+(10+10)xy+25x2

4y^2 + 20xy + 25x^24y2+20xy+25x2