Multiplying Polynomials by Polynomials

Examples, practice problems and steps!

Example 1

Let's multiply the polynomial (3x6+2x5+5) by the polynomial (5x+2)

Step 1 distribute multiply polynomial by polynomial Step 2 Add the resulting Polynomials

15x7 + 10x6 + 25x) + (6x6 + 4x5 + 10) = 15x7 + 16x6 + 4x5+ 25x +10

Example 2

Let's multiply the polynomial(3x6+2x5+5) by the polynomial (4x2 + x + 5)

Step 1 distribute multiply polynomial by polynomial 2 Step 2 Add the resulting Polynomials

(12x8 + 8x7 + 20x2) + (3x7 + 2x6 + 5x) + (15x6 + 10x5 +25)

Answer = 12x8 + 11x7 + 17x6+ 10x5 + 20x2+ 5x+ 25

Practice Problems

Problem 1

Multiply the polynomial(3x+4) by the polynomial(5x4 +7x3 + 5x)

This is similar to example 1

Step 1
Step 2
Add the resulting Polynomials

15x5 + 41x4 + 28x3 + 15x2 + 20x

Problem 2

Multiply (2x7 +4x2 +3x)(3x8+ 2x3 + 15x)

This is similar to example 2

Step 1
Step 2
Add the resulting Polynomials

6x13 + 4x12 + 12x8+ 27x7 + 6x6 + 20x 2 + 15x