Solve (y ^ 3 + 3y ^ 2 + 3y + 1) + (y ^ 3 - 3y ^ 2 + 3y - 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

$$(y^{3}+3y^{2}+3y+1)+(y^{3}-3y^{2}+3y-1)$$

Evaluate

$2y\left(y^{2}+3\right)$

Solution Steps

Combine $y^{3}$ and $y^{3}$ to get $2y^{3}$.

$$2y^{3}+3y^{2}+3y+1-3y^{2}+3y-1$$

Combine $3y^{2}$ and $-3y^{2}$ to get $0$.

$$2y^{3}+3y+1+3y-1$$

Combine $3y$ and $3y$ to get $6y$.

$$2y^{3}+6y+1-1$$

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

$$2y^{3}+6y$$

Factor

$2y\left(y^{2}+3\right)$

Solution Steps

Multiply and combine like terms.

$$2y^{3}+6y$$

Factor out $2$.

$$2\left(y^{3}+3y\right)$$

Consider $y^{3}+3y$. Factor out $y$.

$$y\left(y^{2}+3\right)$$

Rewrite the complete factored expression. Polynomial $y^{2}+3$ is not factored since it does not have any rational roots.

$$2y\left(y^{2}+3\right)$$