# 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 $x^{2}$.

## Review

Methods
• Techniques are methods.  In other words, they are “ways of doing something.”
Area
• Area is a two-dimensional measurement.
• $Area\;=\; x\bullet x=x^{2}$
• That’s why we cannot use the tiles to represent degrees higher than 2.

Operations
• Difference: subtraction
• Product: multiplication
• Quotient: division.

## Notes

• 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: $(3x+2)+(2x+1)$

Answer: $5x+3$

• Trinomial Example

• 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.

• 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.