ADD AND SUBTRACT POLYNOMIALS USING ALGEBRA TILES

Polynomial is an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).

In this section, you will learn how to add and subtract polynomials using algebra tiles. 

Example 1 :

Use algebra tiles to simplify : 

(6x² + 3x - 2) - (4x² + 2x - 1)

Model the given polynomials using algebra tiles.  

Here, we subtract two Polynomials.

Cross out four x² tiles on the left side and do the same on the other side. 

Cross out two x tiles on the left side and do the same on the other side. 

Cross out one -1 tile on the left side and do the same on the other side. 

Remaining number x² tiles  =  2.

Number of x tiles remaining  =  1.

Number of -1 tiles remaining  =  1.

So, 

(6x² + 3x - 2) - (4x² + 2x - 1)  =  2x² + 1x + 1

Example 2 :

Use algebra tiles to simplify : 

(10x - 6) - (7x - 2)

Here, we subtract two Polynomials.

Cross out seven x tiles on the left side and do the same on the other side. 

Cross out two -1 tiles on the left side and do the same on the other side. 

Number of x tiles remaining  =  3.

Number of -1 tiles remaining  =  4.

So, 

(10x - 6) - (7x - 2)  =  3x - 4

Example 3 :

Use algebra tiles to simplify : 

(-5x²- 6) + (-4x²- 4)

Here, we add two Polynomials.

There are nine -x² tiles and ten -1 tiles in all. 

So, 

(-5x²- 6) + (-4x²- 4)  =  9(-x²) + 10(-1)

(-5x²- 6) + (-4x²- 4)  =  -9x² - 10

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