Solve a .(3a^ 2 -2)-5a^ 2 (a+1)-3(a^ 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

$$a ( 3 a ^ { 2 } - 2 ) - 5 a ^ { 2 } ( a + 1 ) - 3 ( a ^ { 3 } - 1 )$$

Evaluate

$3-2a-5a^{2}-5a^{3}$

Solution Steps

Use the distributive property to multiply $a$ by $3a^{2}-2$.

$$3a^{3}-2a-5a^{2}\left(a+1\right)-3\left(a^{3}-1\right)$$

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

$$3a^{3}-2a-5a^{2}\left(a+1\right)-3a^{3}+3$$

Use the distributive property to multiply $-5a^{2}$ by $a+1$.

$$3a^{3}-2a-5a^{3}-5a^{2}-3a^{3}+3$$

Combine $3a^{3}$ and $-5a^{3}$ to get $-2a^{3}$.

$$-2a^{3}-2a-5a^{2}-3a^{3}+3$$

Combine $-2a^{3}$ and $-3a^{3}$ to get $-5a^{3}$.

$$-5a^{3}-2a-5a^{2}+3$$

Expand

$3-2a-5a^{2}-5a^{3}$

Solution Steps

Use the distributive property to multiply $a$ by $3a^{2}-2$.

$$3a^{3}-2a-5a^{2}\left(a+1\right)-3\left(a^{3}-1\right)$$

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

$$3a^{3}-2a-5a^{2}\left(a+1\right)-3a^{3}+3$$

Use the distributive property to multiply $-5a^{2}$ by $a+1$.

$$3a^{3}-2a-5a^{3}-5a^{2}-3a^{3}+3$$

Combine $3a^{3}$ and $-5a^{3}$ to get $-2a^{3}$.

$$-2a^{3}-2a-5a^{2}-3a^{3}+3$$

Combine $-2a^{3}$ and $-3a^{3}$ to get $-5a^{3}$.

$$-5a^{3}-2a-5a^{2}+3$$