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[ x8 - 5x2 ] is not the difference of two squares. [ 5x2 ] is not really a square.
If you do have the difference of two squares, then:
-- Take the square roots of the two terms.
-- The factored form is (sum of the square roots) times (difference of the square roots)
Example:
Let's use . . . [ x8 - 9x2 ] .
The square roots of the terms are . . . [ x4 ] and [ 3x ] .
The factored form is (x4 + 3x) (x4- 3x).
Go ahead and FOIL those factors out and you'll see.
With this particular example, you could also continue, and
factor 'x' out of each of these factors, to wind up with
x2 (x3 + 3) (x3 - 3)
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How do you factor m2 - 9?
-7
How do you factor X squared plus 36?
x2 + 36 cannot be factored. You can only factor the difference of two squares, not the sum.
Factor the expression 100A2 - 49B2?
100a2 - 49b2 is the difference of two perfect squares. Therefore, it is equal to the sum times the difference of the roots: (10a + 7b)(10a - 7b)
What is an expression that contains two perfect squares with one subtracted from the other?
Difference
Can two squares have the same ratio for their scale factor and the ratio of their areas?
Let a represent the scale factor of the two squares. Then it follows that the ratio of the areas is a^2. If these are equal, you get the equation a = a^2, and this is only true for a=0 or a=1. However, the only applicable value for a here is 1. In short, yes, they can, but only if both the scale factor and the ratio of the areas are equal to 1 (i.e. the squares are congruent)
