UNIT 5
Polynomials and Properties of Exponents
LESSON 2
Adding and Subtracting Polynomials
Adding and subtracting polynomials is similar to adding and subtracting numbers. The only difference is that we need to combine the terms with the same variables and powers.
To add or subtract polynomials, we simply combine the like terms by adding or subtracting their coefficients.
Let's look at some examples:
Example 1:
(2x² + 3x - 5) + (4x² - 2x + 7)
To add these two polynomials, we need to combine the like terms.
First, we add the terms with x²:
2x² + 4x² = 6x²
Then, we add the terms with x:
3x - 2x = x
Finally, we add the constant terms:
-5 + 7 = 2
So, the sum of the two polynomials is:
6x² + x + 2
Example 2:
(5x³ - 2x² + x) - (3x³ + 4x² - 2x)
To subtract these two polynomials, we need to distribute the negative sign:
5x³ - 2x² + x - 3x³ - 4x² + 2x
Then, we combine the like terms:
5x³ - 3x³ = 2x³
-2x² - 4x² = -6x²
x + 2x = 3x
So, the difference of the two polynomials is:
2x³ - 6x² + 3x
In summary, to add or subtract polynomials, we need to combine the like terms by adding or subtracting their coefficients. Remember to distribute the negative sign when subtracting polynomials.