Chapter 31

Adding and Subtracting Polynomials Concept Explanation:

Adding and subtracting polynomials involves combining like terms, which are terms that have the same variables raised to the same power. The process is similar to adding and subtracting numbers, except you deal with variables and exponents.

For example, if you have:

You combine the terms that have the same degree (exponent of the variable).

Steps for Adding/Subtracting Polynomials:

1. Arrange the Polynomials: Align like terms by their degrees (if not already aligned).
2. Add/Subtract the Coefficients: Only the coefficients of like terms are added or subtracted.
3. Combine and Simplify: After performing the addition or subtraction, simplify the result.

Common Mistakes:

1. Combining Unalike Terms: Students often try to combine terms with different exponents, which is not allowed.
2. Dropping Negative Signs: When subtracting polynomials, it’s easy to forget to distribute the negative sign across all terms.

Helpful Tips:

• Highlight Like Terms: Using colors or underlining to identify like terms can help prevent errors.
• Keep Exponents in Mind: Remember, only terms with the same exponents can be combined.

Hard Questions:

Q1: Add .

Step-by-Step Solution:

1. Combine like terms:

Answer:

• The result is .

Q2: Subtract .

Step-by-Step Solution:

1. Distribute the negative sign across the second polynomial:

Combine like terms:

Answer:

• The result is .

Q3: Add .

Step-by-Step Solution:

1. Combine like terms:

Answer:

• The result is .

• Angles of Elevation and Depression
• Angles Fundamentals
• Angle of Rotation
• Angle of Intersecting Chords Theorem
• Angle of Intersecting Secants Theorem