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Ch. R - Review of Basic Concepts
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. R - Review of Basic ConceptsProblem 62
Chapter 1, Problem 62

Perform the indicated operations. (x4−3x2+2)−(−2x4+x2−3)(x^4-3x^2+2) - (-2x^4+x^2-3)

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Identify the expression to simplify: \((x^4 - 3x^2 + 2) - (-2x^4 + x^2 - 3)\).
Distribute the subtraction sign across the second polynomial, changing the signs of each term inside the parentheses: \((x^4 - 3x^2 + 2) + (2x^4 - x^2 + 3)\).
Group like terms together: \((x^4 + 2x^4) + (-3x^2 - x^2) + (2 + 3)\).
Combine the coefficients of like terms: add the coefficients of \(x^4\) terms, \(x^2\) terms, and constant terms separately.
Write the simplified expression by putting together the combined terms.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Polynomial Expressions

Polynomial expressions are algebraic expressions consisting of variables raised to whole-number exponents and coefficients. Understanding how to identify terms, degrees, and coefficients is essential for performing operations like addition and subtraction on polynomials.
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Subtraction of Polynomials

Subtracting polynomials involves changing the signs of the terms in the polynomial being subtracted and then combining like terms. Careful attention to distributing the negative sign across all terms is crucial to avoid errors.
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Adding and Subtracting Polynomials

Combining Like Terms

Combining like terms means adding or subtracting terms that have the same variable raised to the same power. This simplifies the expression and is a key step after performing addition or subtraction of polynomials.
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Related Practice
Textbook Question

Factor each polynomial. See Examples 5 and 6. y4-81

Textbook Question

Add or subtract as indicated. Write answers in lowest terms as needed. 318+2143\(\frac{1}{8}\) + 2\(\frac{1}{4}\)

Textbook Question

Let A = {2, 4, 6, 8, 10, 12}, B = {2, 4, 8, 10}, C = {4, 10, 12}, D = {2, 10}, andU = {2, 4, 6, 8, 10, 12, 14}. Determine whether each statement is true or false. A ⊆ C

Textbook Question

Find each product or quotient where possible. -0.5(-0.6)

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Textbook Question

Factor each polynomial. See Examples 5 and 6. x4-16

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Textbook Question

Factor each polynomial. See Examples 5 and 6. 25s4-9t2

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