Question

Find the product:
(4x-5y)^2=
(4x-5y)(4x-5y)=
(4x)(4x)=16x^2
(4x)(-5y)=-20xy
(-5y)(4x)=-20xy
(-5y)(-5y)=25y^2

16x^2-20xy-20xy+25y^2=
16x^2+25y^2

Is this correct?

Answer 1

This part is good

16x^2-20xy-20xy+25y^2

but how did you make the -20xy - 20xy go away!
you can combine them

Answer 2

add "like terms"
like terms have the same variables (letters). Just add their coefficients
-20xy - 20xy = -40xy

Answer 3

ok, so I originally had 16x^2-40xy + 25y^2, doubted myself

Answer 4

you check yourself by replacing x and y with numbers. for example, let x=1 and y=1 (makes it easy)
(4x-5y)^2 becomes (4-5)^2= -1*-1= 1
now try
16x^2-40xy + 25y^2. It becomes 16*1*1-40*1*1+25*1*1 or 16-40+25= 1
on the other hand

16x^2+25y^2 is 16+25= 41 which is definitely not 1

Answer 5

ok, thank you for explaining that. it definitely helps!!:)