Background

Polynomials are expressions of finite length constructed from variables.  Note that the only operations used are addition, subtraction, and non-negative whole number exponents. For example, we know that 2x3 − 7x + 10 is a polynomial but x2 − 3/x + 7x7/2     is not because the second term involves division by the variable x and because the third term contains a non-integer exponent.

Application

8 + 3= 11.

We may add polynomials in the same way by combining like terms. Let us take a look at an example:

Simplify (3x + 4y) + (5x – 2y)

First, we may omit the parentheses and combine like terms.

(3x + 4y) + (5x – 2y)
=  3x + 5y + 5x – 2y

=  3x + 5x + 4y – 2y

8x + 2y

An alternative to adding horizontally is to add vertically. Looking back at the previous example, here

Simplify (3x + 4y) + (5x – 2y)

Each variable shall be placed in its own column. The first column will be the x-column, and the second column will be the y-column:

3x + 4y 5x – 2y

8x + 2y

Note that we get the same solution vertically as we got horizontally.

Practice Problem

Now, let us do a practice problem

Simplify (4x3 + 3x2 – 2x + 7) + (x3 – 2x2 + x – 4)

Solution

Horizontal Method:

(4x3 + 3x2 – 2x + 7) + (x3 – 2x2 + x – 4)

=  4x3 + 3x2 – 2x + 7 + x3 – 2x2 + x – 4
=  4x3 + x3 + 3x2 – 2x2 – 2x + x + 7 – 4
=
5x3 + 1x2 – 1x + 3

Vertical Method

4x3 + 3x2 – 2x + 7 x3 – 2x2 + x – 4

5x3 + 1x2 – 1x + 3

• Subject : Math
• Topic : Algebra 1, Algebra 2, Basic Math Skills / Pre-Algebra