If f(x)=x^2-3x then write an expression for f(x+y)-f(x)

Question

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Answer 1

f(x+y) means to put x+y in for x in f(x)=x^2 - 3x

so f(x+y) = (x+y)^2 - 3(x+y)   = (x+y)(x+y) - 3x - 3y

= x^2 + 2xy + y^2 - 3x - 3y then subtract f(x)

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

= x^2 + 2xy + y^2 - 3x - 3y - x^2 + 3x    combine like terms and final answer is

=2xy + y^2 - 3y