Theorem binom2subi

Description: Expand the square of a subtraction. (Contributed by Scott Fenton, 13-Jun-2013)

	Ref	Expression
Hypotheses	binom2subi.1	|- A e. CC
	binom2subi.2	|- B e. CC
Assertion	binom2subi	|- ( ( A - B ) ^ 2 ) = ( ( ( A ^ 2 ) - ( 2 x. ( A x. B ) ) ) + ( B ^ 2 ) )

Proof

Step	Hyp	Ref	Expression
1		binom2subi.1	|- A e. CC
2		binom2subi.2	|- B e. CC
3		binom2sub	|- ( ( A e. CC /\ B e. CC ) -> ( ( A - B ) ^ 2 ) = ( ( ( A ^ 2 ) - ( 2 x. ( A x. B ) ) ) + ( B ^ 2 ) ) )
4	1 2 3	mp2an	|- ( ( A - B ) ^ 2 ) = ( ( ( A ^ 2 ) - ( 2 x. ( A x. B ) ) ) + ( B ^ 2 ) )