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,
7x2 and +2x2 are like terms,
because they have the same x2.

By the same way,
-3x and +8x are like terms,
because they have the same x (= x1).

Only like terms can be added or subtracted
by adding or subtracting their coefficients.

7x2 and +2x2 are like terms.
So 7x2 + 2x2 = (7 + 2)x2.

-3x and +8x are like terms.
So -3x + 8x = (-3 + 8)x.

So 7x2 - 3x + 2x2 + 8x = (7 + 2)x2 + (-3 + 8)x

Simplify the coefficients.
7 + 2 = 9
-3 + 8 = 5

So 9x2 + 5x is the answer.

Example 2

Example

Solution

3a2 and -a2 are like terms.
So 3a2 - a2 = (3 - 1)a2.

+ab2 and +9ab2 are like terms.
So +ab2 + 9ab2 = +(1 + 9)ab2.

+2ab and -6ab are like terms.
So +2ab - 6ab = +(2 - 6)ab.

ab2 term is written before ab term.
There's a reason.
Usually, the terms are written in descending order.
Both ab2 and ab have the same power a.
But ab2 has the higher power b: b2.
So you should write the ab2 term before the ab term.

So 3a2 + 2ab + ab2 - 6ab + 9ab2 - a2
= (3 - 1)a2 + (1 + 9)ab2 + (2 - 6)ab.

Simplify the coefficients.
3 - 1 = 2
1 + 9 = 10
2 - 6 = -4

So 2a2 + 10ab2 - 4ab is the answer.