## A function B : ℤ x ℤ → ℤ is called 'bilinear' if it satisfies B(x+y,z)=B(x,z) + B(y,z) and also B(x,y+z)=B(x,y) + B(x,z) for all x,y,z ∈ ℤ. Suppose B is bilinear: a) Expand B(x+y,x+y) so that all the addition happens outside of B. b) Show that ∀x

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A function B : ℤ x ℤ → ℤ is called 'bilinear' if it satisfies B(x+y,z)=B(x,z) + B(y,z) and also B(x,y+z)=B(x,y) + B(x,z) for all x,y,z ∈ ℤ. Suppose B is bilinear: a) Expand B(x+y,x+y) so that all the addition happens outside of B. b) Show that ∀x ∈ ℤ, B(x,x)=0 ⇔ ∀x,y ∈ ℤ, B(x,y)= -B(y,x) --

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