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10.2 – Adding and Subtracting Polynomials
Key Terms
 Area – The size of a surface. It is measured in square units.
 Collecting Like Terms – Simplifying an expression by grouping together terms that have the same variables and powers and then adding or subtracting these terms.
 Tiles – Tools that can help add, subtract, multiply, and divide some polynomials.
 Small squares represent 1. Small rectangles represent x. Larger squares represent .
Review
Methods 
 Techniques are methods. In other words, they are “ways of doing something.”

Area 
 Area is a twodimensional measurement.
 That’s why we cannot use the tiles to represent degrees higher than 2.

Operations 
 Sum: addition
 Difference: subtraction
 Product: multiplication
 Quotient: division.

Notes
Adding Polynomials Using Tiles 
 Tiles are labeled using their area (length times width)

 How to Use Tiles to Add Polynomials
 Step 1: Use tiles to show each polynomial.
 Step 2: Combine all the tiles.
 Step 3: Write a polynomial for the combined tiles.
 Binomial Example:
Answer:

Adding Polynomials Side by Side 
 How to Add Polynomials Side by Side
 Step 1: Remove the parentheses.
 Step 2: Collect like terms.
 When you collect like terms in a polynomial, you group terms by degree.
 Step 3: Simplify.

 Example, using the steps (above)
 Another example (using negative terms)
 Remember, minus signs are just negatives!
 Negatives belong to the terms that follow them.

Adding Polynomials Vertically 
 How to Add Polynomials Vertically
 Step 1: Arrange the problem vertically.
 Step 2: Fill in any missing terms using zero coefficients.
 Step 3: Add the polynomials.
 Step 4: Simplify the sum.

 Example, using steps (above)

Subtracting Polynomials Using Tiles 
 How to Use Tiles to Subtract Polynomials
 Step 1: Use tiles to show each polynomial.
 Step 2: Remove subtracted tiles.
 Step 3: Write a polynomial for the tiles left over.

 Example, using steps (above)

Subtracting Polynomials Side by Side 
 How to Subtract Polynomials Side by Side
 Step 1: Use the distributive property to change the subtracted polynomial to an added polynomial.
 Multiply a negative 1 through the 2nd polynomial
 This changes the sign of each term in the 2nd polynomial
 Step 2: Solve it like an addition problem.

 Example, using steps (above)

Subtracting Polynomials Vertically 
 How to Subtract Polynomials Vertically
 Step 1: Make sure the polynomials are written in descending order.
 Step 2: Write the polynomials vertically with the like terms aligned.
 Step 3: Replace any missing terms with terms that have a zero coefficient.
 Step 4: Multiply the bottom polynomials by (1).
 Step 5: Add the polynomials.

 Example, using steps (above). Video has no sound.

Important!
Practice (Apex Study 10.2)
 Try practice problems on Pg 12
 Mandatory: write and answer problems on Pg 9, 15, 19
 2 Quizzes
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