algebra math equation multiply and express the product in simplist form

Hi,

x³ - 27........1
----------.X.-------- =
...8.........x² - 9

The first numerator is the difference of perfect cubes and it factors. The last denominator is the difference of perfect squares and factors.


(x - 3)(x² + 3x + 9)........1
---------------------------.X.---------------- =
....... ..8...... ......... ..(x - 3)(x+3)

Cancel out the x - 3 factor to get:

x² + 3x + 9
---------------- <==ANSWER
8(x+3)

I hope that helps!! :-)

(x^3 - 3^3)/2^3 * 1^2/(x^2 - 3^2)
= (x - 3)(x^2 + 3x + 3^2)/2^3 * 1/(x + 3)(x - 3) (cancel out x - 3)
= (x^2 + 3x + 9)/8 * 1/(x + 3)
= (x^2 + 3x + 9)/8(x + 3)

(x-3)(x^2+3x+9)/8 x 1/(x-3)(x+3) =
(X^2 +3X+9) / 8(x+3)

[1*(x³ - 3³)] / [2³ (x² - 3²)]

(x³ - 3³) / [8 (x² - 3²)]

using the following
a³ – b³ = (a – b)(a² + ab + b²)
a² – b² = (a – b)(a + b)

(x - 3)(x² + 3x + 9) / 8(x - 3)(x + 3)

(x² + 3x + 9) / 8(x + 3)


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