Question

The product of (a − b)(a − b) is a2 − b2.

Sometimes

Always

Never

Answer 1

The answer is: "Sometimes".
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This holds true, for instance, when:
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a = 1 AND b = 1 ;
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when: a = 0 AND b = 0 .
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Answer 2

The product of:

`(a-b)(a+b)` is sometimes equal to
`a^2-b^2`

Explanation:

We will find the product of:

`(a-b)(a+b)` as:

`(a-b)(a+b)=a(a+b)-b(a+b)\\\\(a-b)(a+b)=a^2+ab-ba-b^2\\\\(a-b)(a+b)=a^2-b^2`

This could be done or the result is true if a and b are real numbers.

since in case of matrices this equality might not hold since ba might be not equal to ab and hence the term ab and (-ba) will not cancel out.

Hence, the answer is:

Sometimes.