Carcass wrote:

If \(a<b<0\) which of the following numbers must be positive?

Indicate all such numbers.

A) \(a - b\)

B) \(a^2 - b^2\)

C) \(ab\)

D) \(a^2b\)

E) \(a^2b + ab^2\)

A) \(a - b\)

Given: \(a<b\)

Subtract b from both sides: \(a-b<0\)

This tells us a-b is

NEGATIVEB) \(a^2 - b^2\)

\(a^2 - b^2=(a+b)(a-b)\)

Since a and b are both negative, we know that a+b =

NEGATIVEAnd, we already learned (above) that a-b is

NEGATIVESo, \(a^2 - b^2=(a+b)(a-b)\) = (

NEGATIVE)(

NEGATIVE) =

POSITIVEC) \(ab\)

Since a and b are both negative, we know that ab = (

NEGATIVE)(

NEGATIVE) =

POSITIVED) \(a^2b\)

Since a and b are both negative, we know that\(a^2b=(a)(a)(b)\) = (

NEGATIVE)(

NEGATIVE)(

NEGATIVE) =

NEGATIVEE) \(a^2b + ab^2\)

Factor to get: \(ab(a +b)\)

We already learned (above) that ab is

POSITIVE, and that a-b is

NEGATIVESo, \(ab(a +b)\) = (

POSITIVE)(

NEGATIVE) =

NEGATIVEAnswer: B and C

Cheers,

Brent

_________________

Brent Hanneson – Creator of greenlighttestprep.com

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