Solve (x ^ 4 + 2x ^ 2 + 1) - (x ^ 4 - 2x ^ 2 + 1) | 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

$$(x^{4}+2x^{2}+1)-(x^{4}-2x^{2}+1)$$

Evaluate

$4x^{2}$

Solution Steps

To find the opposite of $x^{4}-2x^{2}+1$, find the opposite of each term.

$$x^{4}+2x^{2}+1-x^{4}+2x^{2}-1$$

Combine $x^{4}$ and $-x^{4}$ to get $0$.

$$2x^{2}+1+2x^{2}-1$$

Combine $2x^{2}$ and $2x^{2}$ to get $4x^{2}$.

$$4x^{2}+1-1$$

Subtract $1$ from $1$ to get $0$.

$$4x^{2}$$

Expand

$4x^{2}$

Solution Steps

To find the opposite of $x^{4}-2x^{2}+1$, find the opposite of each term.

$$x^{4}+2x^{2}+1-x^{4}+2x^{2}-1$$

Combine $x^{4}$ and $-x^{4}$ to get $0$.

$$2x^{2}+1+2x^{2}-1$$

Combine $2x^{2}$ and $2x^{2}$ to get $4x^{2}$.

$$4x^{2}+1-1$$

Subtract $1$ from $1$ to get $0$.

$$4x^{2}$$