# Add and Subtract Polynomials

How to add and subtract the terms of a polynomial: 2 examples and their solutions.

## Example 1

### Example

### Solution

Before solving this, let's see what like terms are.

Like terms are the terms that have the same variable(s) and exponent(s).

In this polynomial,

7x^{2} and +2x^{2} are like terms,

because they have the same x^{2}.

By the same way,

-3x and +8x are like terms,

because they have the same x (= x^{1}).

Only like terms can be added or subtracted

by adding or subtracting their coefficients.

7x^{2} and +2x^{2} are like terms.

So 7x^{2} + 2x^{2} = (7 + 2)x^{2}.

-3x and +8x are like terms.

So -3x + 8x = (-3 + 8)x.

So 7x^{2} - 3x + 2x^{2} + 8x = (7 + 2)x^{2} + (-3 + 8)x

Simplify the coefficients.

7 + 2 = 9

-3 + 8 = 5

So 9x^{2} + 5x is the answer.

## Example 2

### Example

### Solution

3a^{2} and -a^{2} are like terms.

So 3a^{2} - a^{2} = (3 - 1)a^{2}.

+ab^{2} and +9ab^{2} are like terms.

So +ab^{2} + 9ab^{2} = +(1 + 9)ab^{2}.

+2ab and -6ab are like terms.

So +2ab - 6ab = +(2 - 6)ab.

ab^{2} term is written before ab term.

There's a reason.

Usually, the terms are written in descending order.

Both ab^{2} and ab have the same power a.

But ab^{2} has the higher power b: b^{2}.

So you should write the ab^{2} term before the ab term.

So 3a^{2} + 2ab + ab^{2} - 6ab + 9ab^{2} - a^{2}

= (3 - 1)a^{2} + (1 + 9)ab^{2} + (2 - 6)ab.

Simplify the coefficients.

3 - 1 = 2

1 + 9 = 10

2 - 6 = -4

So 2a^{2} + 10ab^{2} - 4ab is the answer.