Solve (5(x)^(2)-2)\times((x)^(2)+3x-1)+(x-1)\times(x)^(3)+3-1) | 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

$$(5 { x }^{ 2 } -2) \times ( { x }^{ 2 } +3x-1)+(x-1) \times { x }^{ 3 } +3-1)$$

Evaluate

$6x^{4}+14x^{3}-7x^{2}-6x+4$

Solution Steps

Use the distributive property to multiply $5x^{2}-2$ by $x^{2}+3x-1$ and combine like terms.

$$5x^{4}+15x^{3}-7x^{2}-6x+2+\left(x-1\right)x^{3}+3-1$$

Use the distributive property to multiply $x-1$ by $x^{3}$.

$$5x^{4}+15x^{3}-7x^{2}-6x+2+x^{4}-x^{3}+3-1$$

Combine $5x^{4}$ and $x^{4}$ to get $6x^{4}$.

$$6x^{4}+15x^{3}-7x^{2}-6x+2-x^{3}+3-1$$

Combine $15x^{3}$ and $-x^{3}$ to get $14x^{3}$.

$$6x^{4}+14x^{3}-7x^{2}-6x+2+3-1$$

Add $2$ and $3$ to get $5$.

$$6x^{4}+14x^{3}-7x^{2}-6x+5-1$$

Subtract $1$ from $5$ to get $4$.

$$6x^{4}+14x^{3}-7x^{2}-6x+4$$

Expand

$6x^{4}+14x^{3}-7x^{2}-6x+4$

Solution Steps

Use the distributive property to multiply $5x^{2}-2$ by $x^{2}+3x-1$ and combine like terms.

$$5x^{4}+15x^{3}-7x^{2}-6x+2+\left(x-1\right)x^{3}+3-1$$

Use the distributive property to multiply $x-1$ by $x^{3}$.

$$5x^{4}+15x^{3}-7x^{2}-6x+2+x^{4}-x^{3}+3-1$$

Combine $5x^{4}$ and $x^{4}$ to get $6x^{4}$.

$$6x^{4}+15x^{3}-7x^{2}-6x+2-x^{3}+3-1$$

Combine $15x^{3}$ and $-x^{3}$ to get $14x^{3}$.

$$6x^{4}+14x^{3}-7x^{2}-6x+2+3-1$$

Add $2$ and $3$ to get $5$.

$$6x^{4}+14x^{3}-7x^{2}-6x+5-1$$

Subtract $1$ from $5$ to get $4$.

$$6x^{4}+14x^{3}-7x^{2}-6x+4$$