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

1 Answer
Jim G.
Oct 22, 2016

#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#

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