বহুুপদীর যোগ

Adding Polynomials

In order to add polynomials together, add together the coefficients of terms with the same exponents. You'll also add constants (terms without variables) together.

Let's take a look of adding polynomials:

$$(x^2+3x-9)+(2x^2-4x+3)+(-7x^2-6x+2)$$

$$\begin{align} &=x^2+3x-9+2x^2-4x+3-7x^2-6x+2\\ &=x^2+2x^2-7x^2+3x-4x-6x-9+3+2\\ &=-4x^2-7x-4 \end{align}$$

A reliable step-by-step approach to adding polynomials together is to:

1. Remove the parentheses and distribute the "$+$" sign (essentially, you are distributing a positive $1$) (OR distribute the "$-$" sign)
2. Rearrange the equation so that like terms are near each other
3. Add the like terms together

Now that you've learned how to add single-variable polynomials, you can learn how to add multi-variable polynomials!

Adding polynomials is pretty straightforward; add the coefficients of corresponding terms. For example: $$\begin{align}&(3x^2+5x-2)+(4x^2-6x+10)\\&=(3+4)x^2+(5-6)x+(-2+10) \\&= 7x^2-x+8\end{align}$$

Now, let's look at a model:

We see a similar idea when we subtract polynomials.

Now, let's do some practice of adding polynomials:

We can extend this concept by adding polynomial with multiple unknowns.

(Video) Adding and Subtracting Polynomials

by PatrickJMT

This video by PatrickJMT shows how you add and subtract polynomials.

$\large{\text{Summary}}$

First, we need to combine like terms. Let's look at an example to see this. Suppose we want to add: $$(x^2+4x+5)+(6x+3)$$

First, we distribute anything outside the parentheses inside. Since there's nothing, we can drop both sets of parentheses. $$\begin{align} &(x^2+4x+5)+(6x+3)\\ &=x^2+4x+5+6x+3 \end{align}$$

Next, we want to group the like terms together. Recall, like terms have the same variable and same exponent. $$\begin{align} &x^2+4x+5+6x+3\\ &=x^2+(4x+6x)+(5+3) \end{align}$$

Then, pull out the variables. In $(4x+6x)$, both have an $x$ so we can pull it out. $$\begin{align} &x^2+(4x+6x)+(5+3)\\ &=x^2+(4+6)x+(5+3) \end{align}$$

Finally, add the coefficients. $$\begin{align} &x^2+(4+6)x+(5+3)\\ &=x^2+10x+8 \end{align}$$