Reduce the Expression: Simplifying (16x^4-4x^3)/(2x)

Question

Reduce the following expression:

$\frac{16x^4-4x^3}{2x}$

Video Solution

Solution Steps

00:00 Simply

00:03 Let's break down 16 into factors 2 and 8

00:07 Let's break down power of 4 into factor to the power of 3 and multiplication by factor

00:12 Let's break down 4 into factors 2 and 2

00:16 Let's break down power of 3 into factor squared times the factor

00:21 Let's mark the common factors

00:45 Let's take out the common factors from the parentheses

01:02 Let's reduce what we can

01:07 And this is the solution to the question

Step-by-Step Solution

Let's simplify the given expression:

$\frac{16x^4-4x^3}{2x}$ Remember that we can reduce complete expressions only when both the numerator and denominator are completely factored into multiplication expressions,

For this, we'll use factorization. We must first determine whether in the numerator we can factor out a common term. Following this we will proceed to reduce the possible expressions in the resulting fraction:

$\frac{16x^4-4x^3}{2x} \\ \frac{4x^3(4x-1)}{2x} \\ \frac{2x^2(4x-1)}{1}\\ \downarrow\\ \boxed{ 2x^2(4x-1)}$ Let's expand the parentheses in the resulting expression and we can therefore determine that the correct answer is answer a.

Answer

$8x^3-2x^2$

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