Which expression is equivalent to (x2 + 11)2 + (x - 5)(x + 5)?
Correct answer: B. x4 + 23x2 + 96
- A. x4 + 23x2 - 14
- B. x4 + 23x2 + 96
- C. x4 + 12x2 +121
- D. x4 + x2 + 146
Explanation
Choice B is correct. The expression (x2 + 11)2 can be written as (x2 + 11)(x2 + 11), which is equivalent to x2(x2 + 11) + 11(x2 + 11). Distributing x2 and 11 to (x2 + 11) yields x4 + 11x2 + 11x2 + 121, or x4 + 22x2 + 121.The expression (x - 5)(x + 5) is equivalent to (x-5)x + (x-5)5. Distributing x and 5 to (x-5) yields x2 - 5x + 5x - 25, or x2 - 25. Therefore, the expression (x2 + 11)2 + (x - 5)(x + 5) is equivalent to (x4 + 22x2 + 121) + (x2 - 25), or x4 + 22x2 + 121 + x2 - 25.Combining like terms in this expression yields x4 + 23x2 + 96.
Report an error
The more specific you are, the faster it gets fixed. A source beats an opinion.
Prefer email? [email protected]
About Quantitative Reasoning
Quantitative reasoning applies arithmetic and basic algebra to numerical relationships, including percentages, ratios, averages, fractions, proportions, profit and loss, rates, time, work and measurement. Questions focus on translating words into equations, choosing an efficient method and checking whether the result is numerically reasonable.
Practise Quantitative Reasoning
625 free Quantitative Reasoning MCQs from Analytical and Logical Reasoning, each with the correct answer and an explanation. Unlimited attempts, no account needed.
Discussion
Stuck on an option, or know a faster way to get there? Ask or explain it here.
No comments yet. Be the first to explain this one.
Exams that ask Analytical and Logical Reasoning questions like this
Analytical and Logical Reasoning is on 27 papers prepared for on TestUstad, and all of them draw the same bank, so this question is worth knowing for every one of them.
More Quantitative Reasoning questions
y > 4x + 8For which of the following tables are all the values of x and their corresponding values of y solutions to the given inequality?
During a portion of a flight, a small airplane's cruising speed varied between 150 miles per hour and 170 miles per hour. Which inequality best represents this situation, where s is the cruising speed, in miles per hour, during this portion of the flight?
The scatterplot shows the relationship between two variables, x and y. Which of the following graphs shows the most appropriate model for the data?
The relationship between two variables, x and y, is linear. For every increase in the value of x by 1, the value of y increases by 8. When the value of x is 2, the value of y is 18. Which equation represents this relationship?
The table shown summarizes the number of employees at each of the 17 restaurants in a town. Which of the following could be the median number of employees for the restaurants in this town?
The right triangle ABC is shown. What is the value of tan A?