MODEL POLYNOMIAL ADDITION AND SUBTRACTION

Algebra tiles can be used to model polynomial addition and subtraction. 

Activity 1

Use algebra tiles to find (2x² - x)  + (x² +3x -1). 

Model : 

Use tiles to represent all terms from both expressions.  

Algebra :

(2x² - x)  + (x² + 3x -1)

Model : 

Rearrange tiles so that like tiles are together. Like tiles are the same size and shape. 

Algebra :

(2x² + x²) + (-x + 3x) - 1

Model : 

Remove any zero pairs. 

Algebra :

3x² - x + x + 2x - 1

Model : 

The remaining tiles represent the sum. 

Algebra :

3x² + 2x - 1

Activity 2

Use algebra tiles to find (2x² + 6)  - 4x². 

Model : 

Use tiles to represent the terms in the first expression. 

Algebra :

2x² + 6

Model : 

To subtract 4x², we have to remove 4 yellow x²-tiles, but there are not enough to do this. Remember that subtraction is the same as adding the opposite, so rewrite

(2x² + 6) - 4x² as (2x² + 6) + (-4x²)

Add 4 red x²-tiles.

Algebra : 

(2x² + 6) + (-4x²)

Model : 

Rearrange tiles so that like tiles are together.

Algebra : 

2x² + (-4x²) + 6

Model : 

Remove zero pairs. 

Algebra : 

2x² + (-2x²) + (-2x²) + 6

Model : 

The remaining tiles represent the difference. 

Algebra : 

-2x² + 6

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