Adding, Subtracting, and Multiplying Polynomials

πŸ§‘Zayn Alazawi πŸ“…July 5th, 2020 πŸ“ŠGrade 11 Math

Let's explore the fundamental operations of adding, subtracting, and multiplying polynomials.

I. Adding Polynomials:

Definition: Adding polynomials involves combining like terms. Like terms are terms with the same variable(s) raised to the same exponent(s).


  1. Identify like terms in each polynomial.
  2. Combine the coefficients of like terms.

Example: \((3x^2βˆ’2x+5)+(2x^2+4xβˆ’1)\)

Solution: Combine like terms: \((3x^2+2x^2)+(βˆ’2x+4x)+(5βˆ’1)\)\(5x^2+2x+4\)

II. Subtracting Polynomials:

Definition: Subtracting polynomials is similar to addition. However, when subtracting, distribute the negative sign to all terms in the second polynomial.


  1. Distribute the negative sign to all terms in the second polynomial.
  2. Follow the steps for adding polynomials.

Example: \((3x^2βˆ’2x+5)βˆ’(2x^2+4xβˆ’1)\)

Solution: Distribute the negative sign: \(3x ^2 βˆ’2x+5βˆ’2x^2 βˆ’4x+1\)

Combine like terms:

\((3x ^2 βˆ’2x ^2 )+(βˆ’2xβˆ’4x)+(5+1)\)

\(x ^2 βˆ’6x+6\)

III. Multiplying Polynomials:

Definition: Multiplying polynomials involves applying the distributive property multiple times.


  1. Multiply each term in the first polynomial by each term in the second polynomial.
  2. Combine like terms.

Example: \((3xβˆ’2)(2x+1)\)

Solution: Use the distributive property: \(3x(2x)+3x(1)βˆ’2(2x)βˆ’2(1)\)

Combine like terms:

\(6x ^2 +3xβˆ’4xβˆ’2\)

\(6x ^2 βˆ’xβˆ’2\)

These operations are crucial in polynomial manipulation and finding solutions to various mathematical problems.


  1. Evaluate:


  2. Apply the distributive property:

    \(2x(3x)+2x(1)βˆ’3(3x)βˆ’3(1) \)


    Combine like terms:

    \(6x ^2 +2xβˆ’9xβˆ’3\)

    \(6x^2βˆ’7xβˆ’3 \)

  3. Evaluate:

    \((4x ^2 βˆ’7x+3)βˆ’(2x ^2 βˆ’4x+2)\)

  4. Distribute the negative sign:

    \(4x ^2 βˆ’7x+3βˆ’2x ^2 +4xβˆ’2\)


    Combine like terms:

    \((4x ^2 βˆ’2x ^2 )+(βˆ’7x+4x)+(3βˆ’2)\)

    \(2x ^2 βˆ’3x+1\)