Polynomial Basics: Learn It 2

Adding and Subtracting Polynomials

Add and Subtract Monomials

When you are adding or subtracting monomials, think of it as grouping together similar items. These ‘like terms’ are expressions that have the same variable raised to the same power. It’s essential to ensure that both the variable and its exponent match before combining them.

When you’re bringing like terms together, remember that only the coefficients (the numbers in front of the variables) get added or subtracted. The exponents (the powers to which the variables are raised) always remain unchanged.
Add: [latex]17{x}^{2}+6{x}^{2}[/latex]

Subtract: [latex]11n-\left(-8n\right)[/latex]

Add and Subtract Polynomials

Adding and subtracting polynomials can be thought of as just adding and subtracting like terms. Look for like terms—those with the same variables with the same exponent. The Commutative Property allows us to rearrange the terms to put like terms together. It may also be helpful to underline, circle, or box like terms.

Find the sum: [latex]\left(4{x}^{2}-5x+1\right)+\left(3{x}^{2}-8x - 9\right)[/latex].

Subtract [latex]\left(9{m}^{2}-7m+4\right) - \left({m}^{2}-3m+8\right)[/latex]

Be careful When subtracting polynomials
[latex]\\[/latex]
When subtracting a polynomial from another, be careful to subtract each term in the second from the first. That is, use the distributive property to distribute the minus sign through the second polynomial.

[latex]\begin{array}{cc}\left(3x^2-2x+9\right)-\left(x^2-4x+5\right)\text{}\hfill &\text{Distribute the negative in front of the parenthesis} \hfill \\ 3x^2-2x+9 -x^2 -\left(-4x\right) - 5\hfill & \text{Be careful when subtracting a negative}.\hfill \\ 3x^2 - x^2 -2x+4x+9-5\hfill & \text{Rearrange terms in descending order of degree} \hfill \\ 2x^2 +2x +4 \hfill & \text{Combine like terms}. \hfill \end{array}[/latex]