1. ## Simplify

How would you simplify this?

$\displaystyle (a-b)^2(a+b)2$

2. Originally Posted by l flipboi l
How would you simplify this?

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

this is what you want?

3. Originally Posted by l flipboi l
How would you simplify this?

$\displaystyle (a-b)^2(a+b)2$
if you meant ...

$\displaystyle (a-b)^2(a+b)^2$ ...

$\displaystyle (a-b)(a-b)(a+b)(a+b)$

$\displaystyle (a-b)(a+b)(a-b)(a+b)$

$\displaystyle (a^2-b^2)(a^2-b^2)$

$\displaystyle (a^2-b^2)^2$

btw, I do not consider this to be "simplification" ... just changing the expression's looks.

4. Originally Posted by l flipboi l
How would you simplify this?

$\displaystyle (a-b)^2(a+b)2$
You can't simplify the expression, you just can change the expression's look (as skeeter did in his post). You don't have a denominator that could be simplified with the expression (example).

5. Originally Posted by felper
You can't simplify the expression, you just can change the expression's look. You don't have a denominator that could be simplified with the expression.
I thought I said that ... ?

anyway, lack of a denominator does not mean an expression cannot be simplified.

6. Originally Posted by skeeter
I thought I said that ... ?

anyway, lack of a denominator does not mean an expression cannot be simplified.
Oh sorry, i've quoted wrongly. I'll edit

7. oops sorry, it should be (a-b)^2(a+b)^2....

is it also possible to have it like this?

and distribute out the terms.

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

8. Originally Posted by skeeter
if you meant ...

$\displaystyle (a-b)^2(a+b)^2$ ...

$\displaystyle (a-b)(a-b)(a+b)(a+b)$

$\displaystyle (a-b)(a+b)(a-b)(a+b)$

$\displaystyle (a^2-b^2)(a^2-b^2)$

$\displaystyle (a^2-b^2)^2$

btw, I do not consider this to be "simplification" ... just changing the expression's looks.
Just wondering, should it be (a-b)(a+b) = (a-b)^2?

(a-b)(a+b)(a+b)(a+b)

9. Originally Posted by l flipboi l
Just wondering, should it be (a-b)(a+b) = (a-b)^2?
No,..

$\displaystyle (a-b)(a+b) = a^2 - b^2 \not = (a-b)^2$