Answer: A - The value of the expression is 0. Use x3 − y3 = (x − y)(x2 + xy + y2 )729x3 − 64y3 = (9x)3 − (4y)3 = (9x − 4y)(81x2 + 36xy + 16y2 ) = = (9 × 4 − 4 × 9)(81 × 42 + 36 × 4 × 9 + 16 × 92 ) = = 0 × (81 × 42 + 36 × 4 × 9 + 16 × 92 ) = 0

PracticeQuiz content is free on an ad-supported model.

Unfortunately, we can't support ad blocker usage because of the impact on our servers. If you'd like to continue, please disable your ad blocker and reload page.

Reload page

SAT Prep

Category - Math

Start a Study Session Sign up for Question of the Day

What is the value of 729x³ − 64y³, if x = 4 and y = 9?

Explanation

Answer: A - The value of the expression is 0. Use x³ − y³ = (x − y)(x² + xy + y² )
729x³ − 64y³ = (9x)³ − (4y)³ = (9x − 4y)(81x² + 36xy + 16y² ) =
= (9 × 4 − 4 × 9)(81 × 4² + 36 × 4 × 9 + 16 × 9² ) =
= 0 × (81 × 4² + 36 × 4 × 9 + 16 × 9² ) = 0

Previous Next

Was this helpful? Upvote!

Start a Study Session Sign up for Question of the Day

Related questions

3 votes

Choose the answer which best rewords the underlined portion. If you think the original wording is best, choose option A.Private debt becoming public debt because of the lack of steady growth and credit availability.
3 votes

The name Jane Goodall is synonymous with chimpanzees. Having devoted her life to observing these animals in their native African homes, she has gained a plethora of information related to these primates. Ironically, Goodall was not always an animal behavioral analyst. But upon completing secretarial school she began working with well-known paleontologist, Louis Leakey, and was given her first assignment to study apes and chimps in Africa. While Dr. Leakey asserted that ancient apes were the descendants of chimps and humans, Goodall did not concur. Her research contradicted Leakey’s and he advised her to pursue her ideas. From there, Jane began to exclusively study chimpanzees and developed an overwhelming desire to spend her time in the jungles learning about these intriguing creatures.What does the word synonymous mean as used in the first sentence of this passage?
3 votes

Adaptation of Edgar Allan Poe’s “The Tell-Tale Heart” Anxiety, dread, apprehension…regardless of what you call it, it remains the same. It consumes me in the morning, during the day, in the evening, and creeps into the darkest hours of the night. Some say it’s a disease. Others regard it more as a choice. Whatever it is; my senses are no longer the same. My hearing is acute; my vision is obsolete. The lightest of touches sends shivers to every nerve in my body. Mad, I may seem, but with every ounce of my faculties, I will replay the events of that unfortunate day. One that suffers as I do is often perplexed with ideas that enter the brain with no real knowledge of when or where they were conceived. This was the case when the fine line between love and hate became entangled in a series of actions that would forever haunt me. An old man and I had met some years back. We became friends, and he was now living in my home. He had wealth, this was true, but it was not my desire. His words were never demeaning, so it was not this that could be blamed for my failed attempts at restricting the desires within my mind. Looking back, I loved this elderly man. But, there amongst the pleasantries of this seemingly normal man - there IT was- his eye, vulture-like, and the constant disturber of my peace. It was obscure to some, but for me, my daily encounter with his eye caused my anxieties to multiply at an alarming rate, requiring response and action. The cloudy blue emptiness of this orb seemed innocent to some, but to me, every time it captured my vision, I became frozen in time. It was only three evenings ago that I decided its coldness would beset me for the final time. Call it the moment when I transitioned from a fiery man with a zest for life to a lunatic. Call it what you may… The old man always went to bed early, especially with the shortening days leading to earlier and earlier sunsets. Every evening, I watched, studied, observed, and even recorded his routine. After only two evenings, I had deemed him predictable, but even amidst such predictability, I wanted to be sure, so I watched him for five more nights. It was on the seventh evening that I had decided this emptiness was going to tranquilize me in fear no more. I moved slowly, cautiously…careful to note that not even a finger had quivered in the generously-sized bed. After inching myself into the room, I fingered the miniscule dagger in the safety net of my pocket. A single groan emanated from his slumber. I began to retract my steps, but there were no more sounds. I knew it had to be now. The old man’s hour had come. Once and for all, I had to see if the destruction of this repulsion could compel me back to sanity. It was this torturous villain that had I sought, launching my dagger into the intricacies of its design. Remorse? None! Pity? None! Repentance? None! He was dead. The eye would frighten me no more. Finally, it remained hidden under the natural blanket of man’s design. I giggled. Perhaps, that was the proof that my sanity was not returning. Then, I heard it…that awful noise. Could anything be worse than the wildness of that peering tool that had teased, taunted, and tormented me upon every meeting? It grew louder, stronger, intensifying…the heart, oh the heart…. Its escalating sound drove me to my knees, screaming out in agony. Begging for release. I tore up the boards. Threw the body underneath. Replaced the boards. Ran outside to clear my mind, my ears, my senses. As I re-entered, the sound remained…a single beating heart following the rhythm of life. Unable to listen to its ghostly repetition, I removed the dagger from my pocket once more. In combining my own life-sustaining liquid with the innocent man’s, for a fleeting moment, I was free from the insanity that had beguiled me. Then I too was nothing more than a memory, encapsulated by the memories of those that would hear my story and know the reality of that unfortunate day. When the author writes that he is “unwilling to succumb to its cries anymore”, (line 44), he is referring to:

Most popular on PracticeQuiz

219 votes

You are attempting to gather information from a patient, but they are having a hard time trying to communicate since they were hit in the throat by a baseball bat. What is the function of the vocal cords? NREMT Advanced EMT
209 votes

An 8-year-old boy named Albert has a 10-year-old brother named Benny. Benny joins the service at 20 leaving Albert feeling bitter that he no longer has a brother to look up to. After 7 years, Albert is finally ready to make up with Benny who has been out of the service for 5 years. How old is Albert now? GED Exam Prep: Math
186 votes

Using motivation from ‘within’ is called ______________. CPCE Exam Prep
177 votes

The lymphatic system contains four organs: Medical Coding Exam Prep
127 votes

“A set of specialized organizational capabilities for providing value to customers in the form of services” is the official definition of: IT Service Management Foundation Practice Test

Ad-Blocker not supported

SAT Prep

Top questions

Related questions

Most popular on PracticeQuiz