- Example of simply polynomial and solving equation
- Question:
- If (x + 1)(x + 2) - (x - 3)(x - 4) = 0, then x = ?

- Solution:
- Step1: simplify the polynomail in the left side of the equation:
- (x + 1)(x + 2) = x
^{2}+ 2x + x + (1)(2) = x^{2}+ 3x + 2 - (x - 3)(x - 4) = x
^{2}- 4x - 3x + (-3)(-4) = x^{2}- 7x + 12 - then
- (x + 1)(x + 2) - (x - 3)(x - 4)
- = x
^{2}+ 3x + 2 - (x^{2}- 7x + 12) - = x
^{2}+ 3x + 2 - x^{2}+ 7x - 12 - = 10x - 10
- Given: (x + 1)(x + 2) - (x - 3)(x - 4) = 0
- then 10x - 10 = 0
- 10x = 10
- x = 1
- so x = 1 is the solution.

- Remark:
- If there is a minus sign in front of parentheses, when revove the parentheses all items inside the parentheses will change sign.
- when move one term to other side of the equation, the item will change sign.

Simplify the left side of the equation. When multiply polynomial, pay attention to the order and sign. If there is a minus sign in front of parenthesis, when remove the parenthesis, each item inside the paranthesis will change sign. when get the standard form of first degree equation ax = b, then x = b/a in which, a and b are different numbers.