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?  Which of these three makes the most sense to you? Explain why.

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(1) Factor the difference of two squares:

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

Note that when you check by multiplication, the terms involving ab cancel.

(2) Factor a perfect square trinomial:

`a^2+2ab+b^2=(a+b)(a+b)=(a+b)^2`

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

(3) Factor the sum/difference of two cubes:

`a^3-b^3=(a-b)(a^2+ab+b^2)`

`a^3+b^3=(a+b)(a^2-ab+b^2)`

You would have to answer the question about sense making for yourself. To...

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(1) Factor the difference of two squares:

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

Note that when you check by multiplication, the terms involving ab cancel.

(2) Factor a perfect square trinomial:

`a^2+2ab+b^2=(a+b)(a+b)=(a+b)^2`

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

(3) Factor the sum/difference of two cubes:

`a^3-b^3=(a-b)(a^2+ab+b^2)`

`a^3+b^3=(a+b)(a^2-ab+b^2)`

You would have to answer the question about sense making for yourself. To me, the perfect square trinomial is easiest to see because I know a geometric interpretation -- draw a square whose sides are a+b -- the square can be partitioned into a square of side a, a square of side b, and 2 rectangles of sides a,b.

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