SOLUTION: Please help I am confused thank You. Check that the following expressions are equivalent using the values x = -2, -1, 0, 1, 2. (12x^2−27)/(3) and −(−2x+3)(2x+3) Pr

Algebra ->  Equations -> SOLUTION: Please help I am confused thank You. Check that the following expressions are equivalent using the values x = -2, -1, 0, 1, 2. (12x^2−27)/(3) and −(−2x+3)(2x+3) Pr      Log On


   

Question 1187429: Please help I am confused thank You.
Check that the following expressions are equivalent using the values x = -2, -1, 0, 1, 2.
(12x^2−27)/(3) and −(−2x+3)(2x+3)
Prove the equivalence of the two expressions in the previous question using algebraic manipulation.
Found 2 solutions by MathLover1, Alan3354:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Check that the following expressions are equivalent using the values
+x+= -2, -1, 0, 1, 2.

%2812x%5E2-27%29%2F3+ and -%28-2x%2B3%29%282x%2B3%29

use +x+=-2

%2812%28-2%29%5E2-27%29%2F3+ ->%2812%2A4-27%29%2F3+->7
and
%28-%28-2%28-2%29%2B3%29%282%28-2%29%2B3%29%29->%28-%284%2B3%29%28-4%2B3%29%29->%28-%284%2B3%29%28-1%29%29 ->7

+x+=-1

%2812%28-1%29%5E2-27%29%2F3+ ->%2812%2A1-27%29%2F3+->-5
and
-%28-2%28-1%29%2B3%29%282%28-1%29%2B3%29->-%282%2B3%29%28-2%2B3%29->%28-5%29%281%29 ->-5

+x+=0

%2812%280%29%5E2-27%29%2F3+ ->%280-27%29%2F3+->-9
and
-%28-2%280%29%2B3%29%282%280%29%2B3%29->-%280%2B3%29%280%2B3%29->%28-3%29%283%29 ->-9

+x+=1

%2812%281%29%5E2-27%29%2F3+ ->%2812%2A1-27%29%2F3+->-5
and
-%28-2%281%29%2B3%29%282%281%29%2B3%29->-%28-2%2B3%29%282%2B3%29->-%28-1%29%285%29 ->-5

+x+=2
%2812%282%29%5E2-27%29%2F3+ ->%2812%2A4-27%29%2F3+->7
and
-%28-2%282%29%2B3%29%282%282%29%2B3%29->-%28-4%2B3%29%284%2B3%29->-%28-1%29%287%29 ->7


since results in both expressions for same x value, it proves the equivalence of the two expressions
so, %2812x%5E2-27%29%2F3+=-%28-2x%2B3%29%282x%2B3%29

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Check that the following expressions are equivalent using the values x = -2, -1, 0, 1, 2.
(12x^2−27)/(3) and −(−2x+3)(2x+3)
------------
Sub the values for x.
---
For x = -2:
--
(12*(-2)^2 - 27)/3 = -(-2*-2 + 3)*(2*-2 +3)
(12*4 - 27)/3 = -(4 + 3)*(-4 + 3)
21/3 = -7*-1
7 = 7
===============
Do the same for the other values.
====================================
Prove the equivalence of the two expressions in the previous question using algebraic manipulation.
------
(12x^2−27)/(3) and −(−2x+3)(2x+3)
4x^2 - 9 = (2x-3)*(2x+3)
4x^2 - 9 = 4x^2 - 9