Solve 3x - 75x ^ 3 | Equatix - Math Solver

Fractions & Decimals

Ratios & Proportions

Basic Number Theory

Integers & Absolute Values

Factors & Multiples

Prime Factorization

Basic Equations & Inequalities

Coordinate Plane & Graphing

Linear Equations & Inequalities

Quadratic Equations

Polynomials & Factoring

Functions & Graphs

Systems of Equations

Trigonometric Functions

Trigonometric Identities & Equations

Right Triangle Trigonometry

Graphing Trigonometric Functions

Limits & Continuity

Derivatives & Applications

Integrals & Applications

Series & Sequences

Multivariable Calculus

Functions & Graphs

Polynomial & Rational Functions

Exponential & Logarithmic Functions

Sequences & Series

Descriptive Statistics

Normal Distribution

Hypothesis Testing

Regression Analysis

Linear Programming

Sets & Counting

Eigenvalues & Eigenvectors

Linear Transformations

Atomic Structure

Thermochemistry

Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$3x-75x^{3}$$

Factor

$3x\left(-5x-1\right)\left(5x-1\right)$

Solution Steps

Factor out $3$.

$$3\left(x-25x^{3}\right)$$

Consider $x-25x^{3}$. Factor out $x$.

$$x\left(1-25x^{2}\right)$$

Consider $1-25x^{2}$. Rewrite $1-25x^{2}$ as $1^{2}-\left(5x\right)^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.

$$\left(1-5x\right)\left(1+5x\right)$$

Reorder the terms.

$$\left(-5x+1\right)\left(5x+1\right)$$

Rewrite the complete factored expression.

$$3x\left(-5x+1\right)\left(5x+1\right)$$

Evaluate

$3x-75x^{3}$