Adding and subtracting polynomials

▶ Adding polynomials

Learn how to simplify polynomials by combining like terms! Discover the power of adding and subtracting terms with the same degree of x. Uncover the magic of removing parentheses and grouping similar terms together to simplify complex expressions. Master the art of polynomial simplification!

⏱ 2:01 💾 1.4 MB License: cc-by-nc-sa Streaming via CDN

▶ Subtracting polynomials

Master the art of adding and subtracting polynomials! Learn how to distribute negative signs across terms, combine like terms, and simplify expressions. This skill is key to understanding algebra and making math easier.

⏱ 2:07 💾 1.5 MB License: cc-by-nc-sa Streaming via CDN

▶ Polynomial subtraction

Learn how to subtract polynomials. Discover how distributing a negative sign changes the signs of all terms in a polynomial. Understand that when you subtract polynomials, you still get a polynomial, showing that the set of polynomials is 'closed' under subtraction.

⏱ 2:50 💾 3.0 MB License: cc-by-nc-sa Streaming via CDN

📄 Adding and subtracting polynomials review

Adding and subtracting polynomials is an exercise in combining like terms. Let's walk through some examples.

Example 1

Simplify.

$(5h^3-8h) +(-2h^3-h^2-2h)$

Rewrite without parentheses:

$\blueD{5h^3-8h} \maroonD{-2h^3-h^2-2h}$

Group like terms:

$(\blueD{5h^3} \maroonD{-2h^3}) \maroonD{-h^2}+(\blueD{-8h} \maroonD{-2h})$

Simplify:

$3h^3-h^2-10h$

Want to see another example? Check out this video.

Example 2

Simplify.

$(-w^3+8w^2-3w) -(4w^2+5w-7)$

Rewrite without parentheses (being careful to distribute the negative):

$\blueD{-w^3+8w^2-3w} \maroonD{-4w^2-5w+7}$

Group like terms:

$ \blueD{-w^3}+(\blueD{8w^2} \maroonD{-4w^2})+(\blueD{-3w} \maroonD{-5w}) \maroonD{+7}$

Simplify:

$-w^3+4w^2-8w+7$

Want to see another example? Check out this video.

Example 3

Express $E+F$ as a trinomial.

$\begin{align}
E &= 6c^2-2c-1 \\
F &= -4c^2+7c+5
\end{align}$

$E+F = (6c^2-2c-1)+( -4c^2+7c+5)$

Rewrite without parentheses and color code like terms:

${\blueD{6c^2} \greenD{-2c} \purpleD{-1} \blueD{-4c^2} \greenD{+7c} \purpleD{+5}}$

Group like terms:

${\blue{(6-4)c^2} + \green{(-2+7)c} + \purple{(-1+5)}}$

Simplify:

${2c^2+5c+4}$

Want to see another example? Check out this video.

Practice

[[☃ graded-group-set 1]]

Want more practice? Check out these exercises: