(x+y)^2 + (x-3y)^2?

Question

could anyone please help me to solve this problem, (x+y)^2 + (x-3y)^2

Answer 1

use foil.... then combine like terms.... x^2+2xy+y^2+x^2-6xy+9y^2=
2x^2-4xy+10y^2

Answer 2

Montgomery Academy question #1 huh?
It's quite simple
(x+y)^2 + (x-3y)^2
=[x^2 + 2xy + y^2] + [x^2 - 6xy + 9y^2]
=x^2 + 2xy + y^2 + x^2 - 6xy + 9y^2
=2x^2 -4xy+10y^2

I didn't know the level of math was so low in USA. Here in India, we learn how to do such problems in middle school.

Answer 3

expanding using the identity (a+b)^2 =a^2+2ab+b^2 and the identity (a-b)^2=a^2-2ab+b^2 the expression
x^2+2xy+y^2+x^2-6xy+9y^2
simplifying
2x^2-4xy+10y^2
2(x^2-2xy+5y^2)

Answer 4

(x+y)^2 + (x-3y)^2
First open out the brackets:
=[(x+y)(x+y)]+[(x-3y)(x-3y)]

=(x^2+xy+yx+y^2)+(x^2-3xy-3yx +9y^2)
=x^2+2xy+y^2+x^2-6xy+9y^2

Put together like configurations
=2x^2-4xy+10y^2 then factor out 2
=2(x^2-2xy+5y^2)

Answer 5

(x+y)^2 + (x-3y)^2
x^2 + y^2 + x^2 - 3y^2
combine like terms
=2x^2 - 2y^2

maybe!

Answer 6

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Answer 7

it is not clear what you want.
If it is expansion and simplification
Here it is
[x+y]^2+[x-3y]^2
=x^2+2xy+y^2
x^2-6xy+9y^2
=2[x^2-2xy+5y^2]

Answer 8

x^2+2xy+y^2+x^2-6xy+9y^2
2x^2-4xy+10y^2

Answer 9

I Think your question needs a right hand side, and maybe another equation

Answer 10

and what do you want to do with that?