What is a^2-b^2/a-b reduced to its lowest terms.

Asked on by hess45

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kborgeson's profile pic

kborgeson | Middle School Teacher | (Level 2) Adjunct Educator

Posted on

a^2 - b^2 is the difference of two perfect squares.  When you have the difference of two squares they can factor into two binomials (a + b)(a - b). 

Your problem then looks like: (a + b)(a - b)/(a - b).   Since it is a division you can then cancel the two binomials that are (a - b). 

This leaves you with the answer:  a + b.  :)

lynn30k's profile pic

lynn30k | High School Teacher | (Level 1) Educator

Posted on

First, you must figure out another way of writing your numerator, a^2-b^2. You can factor this to (a+b)(a-b); those terms, when multiplied, give you your original numerator, because when you multiply them, the ab terms cancel out (one is positive, one is negative.) You then have


Because your terms in the numerator are multiplied by each other, the a-b terms, one in the numerator and one in the denominator equal one, and you are left with a+b as your answer.

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