Prove that for all real numbers a and b, (ab)^2 = a^2b^2.?

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2006-09-13 13:47:21 · 3 answers · asked by TehEagle 1 in Science & Mathematics ➔ Mathematics

Well, (ab)^2 = abab = a(ba)b.
Since ba = ab,
a(ba)b = a(ab)b =a^2b^2.
Note how this depends on the commutative
law of multiplication.

2006-09-13 14:15:20 · answer #1 · answered by steiner1745 7 · 0⤊ 0⤋

Distributive Property of Equality.

2006-09-13 20:57:36 · answer #2 · answered by Spectator 2 · 0⤊ 1⤋

(a*b)^2 = (a*b)*(a*b)
(a*b)*(a*b) = (a*b*a*b)
(a*b*a*b) = (a*a)*(b*b)
(a*a)*(b*b) = a^2*b^2

2006-09-13 20:53:49 · answer #3 · answered by Jeff S 2 · 0⤊ 0⤋