Question

Simplify.$\left(3 x^{2}-5 y^{2}-2 x y\right)-\left(4 x^{2}+8 y^{2}-9 x y\right)$

Name: Problem 46, Chapter 5: Intermediate Algebra for College Students
Uploaded: 2020-06-20T21:38:33-08:00
Duration: 50 s
Channel: Matt Gibson
Description: Simplify.(3 x^2-5 y^2-2 x y)-(4 x^2+8 y^2-9 x y)

   Simplify.$\left(3 x^{2}-5 y^{2}-2 x y\right)-\left(4 x^{2}+8 y^{2}-9 x y\right)$

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 5, Problem 46

Instant Answer

Solved by Expert Matt Gibson

06/20/2020

Step 1

First, let's distribute the negative sign to the terms inside the second parentheses: $3x^2 - 5y^2 - 2xy - (4x^2 + 8y^2 - 9xy) = 3x^2 - 5y^2 - 2xy - 4x^2 - 8y^2 + 9xy$ Now, let's combine like terms: Show more…

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Simplify.$\left(3 x^{2}-5 y^{2}-2 x y\right)-\left(4 x^{2}+8 y^{2}-9 x y\right)$

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Key Concepts

Polynomial Operations

This refers to the process of performing arithmetic operations, such as addition and subtraction, on polynomials. It involves applying the distributive property, organizing the terms, and then carefully combining like terms to simplify the expression.

Distributive Property

This property allows one to multiply a single term across terms within parentheses. In the context of polynomial subtraction, it ensures the correct distribution of the negative sign to each term in the expression being subtracted, which is critical for maintaining accuracy.

Combining Like Terms

This involves grouping together terms that have the same variables raised to the same power and then adding or subtracting their coefficients. It is a fundamental step in simplifying algebraic expressions, as it reduces the expression to its simplest form.

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