Add and subtract polynomials

key notes:

Polynomials:

• A polynomial is an algebraic expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication, but not division by a variable.
• Examples of polynomials: 3�2+2�−53x2+2x−5, 4�3−2�+74y3−2y+7.

Like Terms:

• Terms are terms that have the same variable(s) raised to the same exponent(s).
• Example: 3�23x2 and 2�22x2 are like terms.

Adding Polynomials:

• To add polynomials, combine like terms by adding or subtracting their coefficients.
• Example: (3�2+2�−5)+(4�2−7�+1)=7�2−5�−4(3x2+2x−5)+(4x2−7x+1)=7x2−5x−4.

Subtracting Polynomials:

• To subtract polynomials, distribute the subtraction sign across each term in the second polynomial, then add.
• Example: (3�2+2�−5)−(4�2−7�+1)=−1�2+9�−6(3x2+2x−5)−(4x2−7x+1)=−1x2+9x−6.

Be Careful with Signs:

• Pay attention to signs when combining or subtracting terms.
• Double-check signs in each step to avoid errors.

Zero Pairs:

• When adding or subtracting, look for zero pairs (terms that cancel each other out).
• Example: 2�−2�=02x−2x=0, so these terms create a zero pair.

Examples:

• (2�2+3�−1)+(4�2−2�+5)=6�2+�+4(2x2+3x−1)+(4x2−2x+5)=6x2+x+4
• (5�3+2�2−3�)−(2�3−�2+7�)=3�3+3�2−10�(5y3+2y2−3y)−(2y3−y2+7y)=3y3+3y2−10y

Practice:

• Practice adding and subtracting polynomials with various examples to reinforce understanding.

Learn with an example

let’s practice!🖊️