Theorem subsqi

Description: Factor the difference of two squares. (Contributed by NM, 7-Feb-2005)

	Ref	Expression
Hypotheses	binom2.1	⊢ 𝐴 ∈ ℂ
	binom2.2	⊢ 𝐵 ∈ ℂ
Assertion	subsqi	⊢ ( ( 𝐴 ↑ 2 ) − ( 𝐵 ↑ 2 ) ) = ( ( 𝐴 + 𝐵 ) · ( 𝐴 − 𝐵 ) )

Proof

Step	Hyp	Ref	Expression
1		binom2.1	⊢ 𝐴 ∈ ℂ
2		binom2.2	⊢ 𝐵 ∈ ℂ
3		subsq	⊢ ( ( 𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ ) → ( ( 𝐴 ↑ 2 ) − ( 𝐵 ↑ 2 ) ) = ( ( 𝐴 + 𝐵 ) · ( 𝐴 − 𝐵 ) ) )
4	1 2 3	mp2an	⊢ ( ( 𝐴 ↑ 2 ) − ( 𝐵 ↑ 2 ) ) = ( ( 𝐴 + 𝐵 ) · ( 𝐴 − 𝐵 ) )