Table of contents
- 0. Review of Algebra4h 16m
- 1. Equations & Inequalities3h 18m
- 2. Graphs of Equations43m
- 3. Functions2h 17m
- 4. Polynomial Functions1h 44m
- 5. Rational Functions1h 23m
- 6. Exponential & Logarithmic Functions2h 28m
- 7. Systems of Equations & Matrices4h 6m
- 8. Conic Sections2h 23m
- 9. Sequences, Series, & Induction1h 19m
- 10. Combinatorics & Probability1h 45m
0. Review of Algebra
Polynomials Intro
5: minutes
Problem 83b
Textbook Question
Textbook QuestionIn Exercises 83–90, perform the indicated operation or operations. (3x+4y)^2−(3x−4y)^2
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Difference of Squares
The difference of squares is a fundamental algebraic identity that states that for any two terms a and b, the expression a^2 - b^2 can be factored into (a - b)(a + b). This concept is crucial for simplifying expressions that involve the subtraction of two squared terms, allowing for easier computation and understanding of the underlying structure of the equation.
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Binomial Expansion
Binomial expansion refers to the process of expanding expressions that are raised to a power, particularly those in the form (a + b)^n. The expansion can be achieved using the Binomial Theorem, which provides a formula for calculating the coefficients of the terms in the expansion. Understanding this concept is essential for accurately expanding the squared terms in the given expression.
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Algebraic Manipulation
Algebraic manipulation involves the application of various algebraic rules and properties to simplify or rearrange expressions and equations. This includes operations such as factoring, distributing, and combining like terms. Mastery of algebraic manipulation is necessary to effectively perform the indicated operations in the problem, leading to a correct and simplified result.
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