(3x+2x^4-3x^3-2) (1-x^2)

Jasonbradley

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Jun 16, 2024

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Multiplying Polynomials: (3x + 2x⁴ - 3x³ - 2)(1 - x²)

This article will guide you through multiplying the polynomials (3x + 2x⁴ - 3x³ - 2) and (1 - x²). We will use the distributive property, also known as the FOIL method, to achieve this.

The FOIL Method

FOIL stands for First, Outer, Inner, Last. It's a mnemonic device for remembering how to multiply two binomials. We will apply this method to each term of the first polynomial:

Step 1: First

Multiply the first terms of each polynomial: (3x) * (1) = 3x

Step 2: Outer

Multiply the outer terms of each polynomial: (3x) * (-x²) = -3x³

Step 3: Inner

Multiply the inner terms of each polynomial: (2x⁴) * (1) = 2x⁴

Step 4: Last

Multiply the last terms of each polynomial: (2x⁴) * (-x²) = -2x⁶

Step 5: Repeat for Remaining Terms

We need to repeat the FOIL method for the remaining terms of the first polynomial (-3x³ and -2):

• (-3x³) * (1) = -3x³
• (-3x³) * (-x²) = 3x⁵
• (-2) * (1) = -2
• (-2) * (-x²) = 2x²

Combining Like Terms

Now, we have:

3x - 3x³ + 2x⁴ - 2x⁶ - 3x³ + 3x⁵ - 2 + 2x²

Combining like terms:

-2x⁶ + 3x⁵ + 2x⁴ - 6x³ + 2x² + 3x - 2

Final Answer

Therefore, the product of (3x + 2x⁴ - 3x³ - 2) and (1 - x²) is -2x⁶ + 3x⁵ + 2x⁴ - 6x³ + 2x² + 3x - 2.