Perform the indicated operations. (10m^4-4m^2)/2m

Question

Accepted Answer

Hello today we're going to be finding the quotient of the given expression. So what we are given is 49 B to the eighth minus 21 B to the fourth divided by seven B squared. Now, in order to start this problem, let's go ahead and simplify the given numerator. We can simplify the numerator by determining the greatest common factor between the two given terms. See here 49 21 are both divisible by seven. So we can factor out a seven from the numerator and we have B to the eighth and B to the fourth in both terms in the numerator, both of the terms have at least four instances of B. So we can factor out a B to the fourth from the numerator. So if we factor out seven B to the fourth what we are left with is seven B to the fourth times the quantity seven B to the fourth minus three. And this is going to be divided by seven B squared. Now notice that we have seven in both the numerator and denominator we can just go ahead and cancel out the sevens and we have B to the fourth in the numerator and B squared in the denominator. There are at least two instances in both the numerator and denominator. So we can subtract B squared from both the numerator and denominator, that's going to cancel out the b squared in the denominator and that's going to leave us with b squared in the numerator. And what we are left with is b squared times the quantity seven B to the fourth minus three. And if we redistribute B squared into the quantity seven B to the fourth minus three, what this gives us is seven B to the six minus three B squared. And this is going to be the quotient for the given expression. And with that being said, the answer to this problem is going to be D. So I hope this video helps you in understanding how to approach this problem and I'll go ahead and see you all in the next video.

Perform the indicated operations. (10m^4-4m^2)/2m

Key Concepts

Polynomial Operations

Factoring

Rational Expressions

Watch next