(-4x^2-5x-1)(4x^2-6x-2)

Jasonbradley

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Jun 16, 2024

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Multiplying Binomials: (-4x^2 - 5x - 1)(4x^2 - 6x - 2)

This article will guide you through multiplying the two binomials: (-4x^2 - 5x - 1)(4x^2 - 6x - 2). We'll use the distributive property and then simplify the resulting expression.

The Distributive Property

The distributive property states that a(b + c) = ab + ac. We can apply this to multiplying binomials by thinking of each binomial as a single term.

Let's break down the multiplication:

1. Distribute the first term of the first binomial:

   • (-4x^2)(4x^2 - 6x - 2) = -16x^4 + 24x^3 + 8x^2

2. Distribute the second term of the first binomial:

   • (-5x)(4x^2 - 6x - 2) = -20x^3 + 30x^2 + 10x

3. Distribute the third term of the first binomial:

   • (-1)(4x^2 - 6x - 2) = -4x^2 + 6x + 2

Now, we have the following expression:

-16x^4 + 24x^3 + 8x^2 - 20x^3 + 30x^2 + 10x - 4x^2 + 6x + 2

Combining Like Terms

Finally, we combine the like terms to get our simplified answer:

-16x^4 + 4x^3 + 34x^2 + 16x + 2

Therefore, the product of (-4x^2 - 5x - 1) and (4x^2 - 6x - 2) is -16x^4 + 4x^3 + 34x^2 + 16x + 2.