Question

Simplify.$\left(-k^{3}+3 k^{2}-k-4\right)-\left(4 k^{3}+8 k+3\right)$

Name: Problem 41, Chapter 5: Intermediate Algebra for College Students
Uploaded: 2021-07-17T03:21:01-08:00
Duration: 55 s
Channel: Sherrie Fenner
Description: Simplify.(-k^3+3 k^2-k-4)-(4 k^3+8 k+3)

   Simplify.$\left(-k^{3}+3 k^{2}-k-4\right)-\left(4 k^{3}+8 k+3\right)$

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 5, Problem 41

Instant Answer

Solved by Expert Sherrie Fenner

07/17/2021

Step 1

First, let's distribute the negative sign to the terms inside the second parentheses: $-k^3 + 3k^2 - k - 4 - (4k^3 + 8k + 3) = -k^3 + 3k^2 - k - 4 - 4k^3 - 8k - 3$ Now, let's combine like terms: Show more…

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Simplify.$\left(-k^{3}+3 k^{2}-k-4\right)-\left(4 k^{3}+8 k+3\right)$

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Key Concepts

Polynomial Subtraction

This concept involves subtracting one polynomial from another, which requires changing the sign of each term in the polynomial being subtracted and then combining like terms. It is a fundamental operation in algebra that ensures accurate manipulation of expressions.

Distributive Property

The distributive property allows one to multiply a factor across terms inside parentheses. In the context of polynomial subtraction, it is used to correctly apply the negative sign to all terms in the subtracted expression, thereby preventing mistakes in sign handling.

Combining Like Terms

Once the distributive property has been applied, terms that contain the same variables raised to the same powers can be combined. This process simplifies the polynomial into a more manageable form by consolidating coefficients of similar terms.

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