Solve (6x ^ 2 + 12x + 5) - (x ^ 3 + 4x ^ 2 + 6x + 1) + (2x ^ 2 + 6x + 7) | 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

$$(6x^{2}+12x+5)-(x^{3}+4x^{2}+6x+1)+(2x^{2}+6x+7)$$

Evaluate

$11+12x+4x^{2}-x^{3}$

Solution Steps

To find the opposite of $x^{3}+4x^{2}+6x+1$, find the opposite of each term.

$$6x^{2}+12x+5-x^{3}-4x^{2}-6x-1+2x^{2}+6x+7$$

Combine $6x^{2}$ and $-4x^{2}$ to get $2x^{2}$.

$$2x^{2}+12x+5-x^{3}-6x-1+2x^{2}+6x+7$$

Combine $12x$ and $-6x$ to get $6x$.

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

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

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

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

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

Combine $6x$ and $6x$ to get $12x$.

$$4x^{2}+12x+4-x^{3}+7$$

Add $4$ and $7$ to get $11$.

$$4x^{2}+12x+11-x^{3}$$

Expand

$11+12x+4x^{2}-x^{3}$

Solution Steps

To find the opposite of $x^{3}+4x^{2}+6x+1$, find the opposite of each term.

$$6x^{2}+12x+5-x^{3}-4x^{2}-6x-1+2x^{2}+6x+7$$

Combine $6x^{2}$ and $-4x^{2}$ to get $2x^{2}$.

$$2x^{2}+12x+5-x^{3}-6x-1+2x^{2}+6x+7$$

Combine $12x$ and $-6x$ to get $6x$.

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

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

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

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

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

Combine $6x$ and $6x$ to get $12x$.

$$4x^{2}+12x+4-x^{3}+7$$

Add $4$ and $7$ to get $11$.

$$4x^{2}+12x+11-x^{3}$$