Textbook Question
In Exercises 103–114, factor completely. (x+y)4−100(x+y)2
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 112
In Exercises 111–120, use the order of operations to simplify each expression. 102−100÷52⋅2−3
Verified step by step guidance1
Start by identifying the order of operations, which follows the PEMDAS rule: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
Evaluate the exponents first. In the expression, calculate and .
Perform the division and multiplication next. Divide by the result of , then multiply the result by .
Subtract the result of the division and multiplication from .
Finally, subtract from the previous result to simplify the expression completely.
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.
Order of Operations
The order of operations is a set of rules that dictates the sequence in which mathematical operations should be performed to ensure consistent results. The acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)) is commonly used to remember this order. Following these rules is crucial for simplifying expressions correctly.
Recommended video:
Guided course
8:38
Performing Row Operations on Matrices
Exponents
Exponents represent repeated multiplication of a number by itself. For example, 10^2 means 10 multiplied by itself, resulting in 100. Understanding how to evaluate exponents is essential for simplifying expressions that include them, as they can significantly affect the outcome of calculations.
Recommended video:
Guided course
04:06Rational Exponents
Division and Multiplication
Division and multiplication are inverse operations that are performed from left to right in the order of operations. In expressions, they are treated with equal precedence, meaning that when both operations appear, you perform them in the order they occur from left to right. This is important for accurately simplifying expressions that involve these operations.
Recommended video:
03:42Finding Zeros & Their Multiplicity
Related Practice
Textbook Question
In Exercises 107–114, simplify each exponential expression. Assume that variables represent nonzero real numbers. (3x−4 y z−7)(3x)−3
2
views
Textbook Question
Multiply or divide as indicated. [(x^2+6x+9)(x+3)]/[(x^2-4)(x-2)]
1
views
Textbook Question
In Exercises 111–114, simplify each expression. Assume that all variables represent positive numbers. (x−5/4y1/3x−3/4)−6
3
views
Textbook Question
In Exercises 111–114, simplify each expression. Assume that all variables represent positive numbers. (49x−2y4)−1/2(xy1/2)
3
views
Textbook Question
Multiply or divide as indicated. [(x^2-5x-24)/(x^2-x-12)]/[(x^2-10x+16)/(x^2+x-6)]