**Multiplication of Two Polynomials**

Two polynomials can be multiplied by using the distributive property as many times as needed. It is the same as shown for two binomials.

**Examples**

**Example 1**

Multiply (x + 2)(x ^{2} + 5x - 6).

**Solution 1**

Multiplication of polynomials can be performed vertically. The process is similar to multiplying whole numbers.

**Example 2**

Multiply (x + 2)(x ^{2} + 5x - 6) vertically.

**Solution 2**

**Example 3**

Multiply (x ^{2} + 3x - 8)(3x - 5) vertically.

**Solution 3**

**Math Note:** Be sure to place like terms under each other when multiplying vertically.

**Multiplication of Two Polynomials Practice Problems**

**Practice**

Multiply:

1. (x ^{2} + 3x + 2)(x + 1)

2. (3x ^{2} + 2x + 5)(x -6)

3. (2x ^{2} + 4x -1)(2x - 3)

4. (x ^{3} - 2x ^{2} + 2x + 1)(x - 5)

5. (x ^{2} + 2x + 7)(x ^{2} - x -6)

**Answers**

1. x ^{3} + 4x ^{2} + 5x + 2

2. 3x ^{3} - 16x ^{2} - 7x - 30

3. 4x ^{3} + 2x ^{2} - 14x + 3

4. x ^{4} - 7x ^{3} + 12x ^{2} - 9x - 5

5. x ^{4} + x ^{3} - x ^{2} - 19x - 42

Practice problems for these concepts can be found at: Operations With Monomials And Polynomials Practice Test.

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