Multiplying Polynomials by Polynomials

Examples, practice problems and steps!

Example 1

Let's multiply the polynomial $$(3x^6 + 2x^5 + 5)$$ by the polynomial (5x + 2).

Step 1

Distribute.

multiply polynomial by polynomial Step 2

Add the resulting Polynomials

$$( 15x^7 + 10x^6 + 25x) + (6x^6 + 4x^5 + 10) = 15x^7 + 16x^6 + 4x^6 + 25x + 10 $$

$$( 15x^7 + 10x^6 + 25x) + (6x^6 + 4x^5 + 10) \\ = 15x^7 + 16x^6 + 4x^6 + 25x + 10 $$

Example 2

Let's multiply the polynomial$$(3x^6 + 2x^5 + 5)$$ by $$(4x^2 + x + 5)$$.

Step 1

Distribute.

multiply polynomial by polynomial 2 Step 2

Add the resulting Polynomials.

$$ (12x^8 + 8x^7 + 20x^2) + (3x^7 + 2x^6 + 5x) + (15x7^6+ 10x^5 + 25) \\ = \boxed{ 12x^8 + 11x^7 + 17x^6 + 10x^5 + 20x^2 + 5x + 25} $$

$$ (12x^8 + 8x^7 + 20x^2) + (3x^7 + 2x^6 + 5x) + (15x7^6+ 10x^5 + 25) \\ = \boxed{ 12x^8 + 11x^7 + 17x^6 + 10x^5 + 20x^2 + 5x + 25} $$

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