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How do you factor the difference of two squares?

How do you factor the perfect square trinomial? How do you factor the sum and
difference of two cubes?

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Kirill Z. | Physics, math tutor with great knowledge and teaching skillsPhysics, math tutor with great knowledge...
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a2-b2=(a-b)*(a+b). You can check it by simply multiplying the first parentheses and the second ones. You will end up with a2-ab+ab-b2=a2-b2.

If a trinomial is a perfect square, it shall be of the form a2±2ab+b2. Then it is factored as (a±b)*(a±b).

As for the sum and difference of two cubes, the formulas are as follows:

a3+b3=(a+b)*(a2-ab+b2).

a3-b3=(a-b)*(a2+ab+b2).

Again, you can check it by multiplication.