Multiplying Polynomials by Polynomials

Example 1

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

Step 1) distribute

Step 2) Add the resulting Polynomials

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

Example 2

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

Step 1) distribute

Step 2) Add the resulting Polynomials

(12x8 + 8x7 + 20x2) + (3x7 + 2x6 + 5x) + (15x6 + 10x5 +25) Answer = 12x8 + 11x7 + 17x6+ 10x5 + 20x2+ 5x+ 25

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Problem 1)

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

Step 1

This is similar to example 1.

Step 1) distribute

Step 2

Step 2) Add the resulting Polynomials

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

Problem 2)

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

Step 1

This is similar to example 2.

Step 1) distribute

Step 2

Step 2) Add the resulting Polynomials

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