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0x0=0

Q: Ab equals 0 if and only if a equals 0 or b equals 0?

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ab = 0 if and only if (a = 0 or b = 0)

That factors to (a + 1)(a + b) a = -1, -b b = -a

ab=1a+1b a is equal to either 0 or two, and b is equal to a

No, A+B is left as A+B AB would be A x B

15

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6.7

0

Assuming that cross means 'divide' B is equal to 0

ab = 0 if and only if (a = 0 or b = 0)

No. A times B = AB

That factors to (a + 1)(a + b) a = -1, -b b = -a

ab=1a+1b a is equal to either 0 or two, and b is equal to a

C minus B equals AB

No, A+B is left as A+B AB would be A x B

15

Here is a proof. Let a and b be any two real numbers. Consider the number x defined as x = ab + (-a)(b) + (-a)(-b). We can write this out differently as x = ab + (-a)[ (b) + (-b) ] Then, by factoring out -a , we find that x= ab + (-a)(0) = ab + 0 = ab. Also, x = [ a + (-a) ]b + (-a)(-b) And by factoring out b, we find that x=0 * b + (-a)(-b) = 0 + (-a)(-b) = (-a)(-b). Therefore x = ab and x = (-a)(-b) Then, by the transitivity of equality, we have ab = (-a)(-b).

8 1/3 = ab^-1, 1.8 =ab^2