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

2 Answers
MrsRudolph221
Jan 21, 2017

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#

smendyka
Jan 21, 2017

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#

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