Textbook Question
Write each number in scientific notation. 0.0083
1050
views
Ch. P - Fundamental Concepts of Algebra
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
Not the one you use?Change textbookSelect a different textbook
Table of contents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Chapter 1, Problem 83
In Exercises 83–90, perform the indicated operation or operations. (3x+4y)2−(3x−4y)2
Verified step by step guidance1
Recognize that the given expression involves the difference of two squares: \((3x + 4y)^2 - (3x - 4y)^2\). The difference of squares formula is \(a^2 - b^2 = (a - b)(a + b)\).
Identify \(a = (3x + 4y)\) and \(b = (3x - 4y)\) in the expression. Substitute these into the difference of squares formula.
Apply the formula: \((3x + 4y) - (3x - 4y)\) and \((3x + 4y) + (3x - 4y)\). Simplify each term inside the parentheses.
Simplify \((3x + 4y) - (3x - 4y)\) to \(8y\) and \((3x + 4y) + (3x - 4y)\) to \(6x\).
Multiply the simplified terms: \(8y \cdot 6x\). This gives the final simplified expression, which you can calculate if needed.
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
5mWas this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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 states that (a + b)^n = Σ (n choose k) * a^(n-k) * b^k, where k ranges from 0 to n. This concept is essential for simplifying expressions like (3x + 4y)^2.
Recommended video:
Guided course
03:41
Special Products - Cube Formulas
Difference of Squares
The difference of squares is a specific algebraic identity that states a^2 - b^2 = (a - b)(a + b). This identity is useful for factoring expressions where two squared terms are subtracted. In the given problem, recognizing that the expression can be treated as a difference of squares will simplify the calculation significantly.
Recommended video:
06:24Solving Quadratic Equations by Completing the Square
Factoring
Factoring is the process of breaking down an expression into simpler components, or factors, that when multiplied together yield the original expression. This technique is crucial in algebra for simplifying expressions and solving equations. In this case, after applying the difference of squares, factoring will help in obtaining the final simplified form of the expression.
Recommended video:
Guided course
04:36Factor by Grouping
Related Practice
Textbook Question
Find each product. (x+7y)(3x-5y)
1127
views
Textbook Question
State the name of the property illustrated. 1/(x+3) (x+3)=1, x≠−3
1101
views
Textbook Question
Perform the indicated operations. Indicate the degree of the resulting polynomial.
1187
views
Textbook Question
In Exercises 65–92, factor completely, or state that the polynomial is prime. 20y4−45y2
939
views
Textbook Question
In Exercises 83–90, perform the indicated operations. Simplify the result, if possible. (2−6/(x+1))(1 + 3/(x−2))
90
views