Quadratic Expression
*The general form of a quadratic expression in one variable is:ax² + bx +c
where x is the variable, a v and c are constants and a≠0.
- Addition and Subtraction of Quadratic Expressions
a) Example: 4x² + 2x²
Therefore, 4x² + 2x² =6x²
b) Example: 4x² + (-2x² )
Therefore, 4x² + (-2x² ) =2x²
c) Example: -4x² -2x+3x² +x+2
First, you would have to group like terms together
= -4x² + 3x² -2x+x+2
Then, you solve it.
= -x² -x+2
- Negative of a Quadratic Equation
-To find the negative of a quadratic expression, we flip all signs.
a) Example: -(2x² +x-1)
Therefore, -(2x² +x-1) = -2x² -x+1
*We can also simplify quadratic expressions involving the negative of a quadratic expression.
b) (2x² - 3x +1) - (x²-2x-3)
Start by expanding the right part
= 2x² - 3x +1 - x²+2x+3
Then grouping like terms together
= 2x² - x² - 3x + 2x +1 + 3
= x² - x + 4
- Expansion and Simplification of Simple Quadratic Expressions
a ) -x² -x +2 + 3(x² + x - 1) = -x² - x + 2 + 3x² +3x - 3 (expand)
= -x² + 3x² - x + 3x + 2 - 3 (group like terms)
= 2x² + 2x - 1
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