Solve a/3 * (a + 2) * (- a)/2 * (a - 1) - 2a + 3 | 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

$$\frac{a}{3}(a+2)\frac{-a}{2}(a-1)-2a+3$$

Evaluate

$\frac{-\left(a-1\right)\left(a+2\right)a^{2}-12a+18}{6}$

Short Solution Steps

Express $\frac{a}{3}\left(a+2\right)$ as a single fraction.

$$\frac{a\left(a+2\right)}{3}\times \frac{-a}{2}\left(a-1\right)-2a+3$$

Multiply $\frac{a\left(a+2\right)}{3}$ times $\frac{-a}{2}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{a\left(a+2\right)\left(-a\right)}{3\times 2}\left(a-1\right)-2a+3$$

Express $\frac{a\left(a+2\right)\left(-a\right)}{3\times 2}\left(a-1\right)$ as a single fraction.

$$\frac{a\left(a+2\right)\left(-a\right)\left(a-1\right)}{3\times 2}-2a+3$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $-2a+3$ times $\frac{3\times 2}{3\times 2}$.

$$\frac{a\left(a+2\right)\left(-a\right)\left(a-1\right)}{3\times 2}+\frac{\left(-2a+3\right)\times 3\times 2}{3\times 2}$$

Since $\frac{a\left(a+2\right)\left(-a\right)\left(a-1\right)}{3\times 2}$ and $\frac{\left(-2a+3\right)\times 3\times 2}{3\times 2}$ have the same denominator, add them by adding their numerators.

$$\frac{a\left(a+2\right)\left(-a\right)\left(a-1\right)+\left(-2a+3\right)\times 3\times 2}{3\times 2}$$

Do the multiplications in $a\left(a+2\right)\left(-a\right)\left(a-1\right)+\left(-2a+3\right)\times 3\times 2$.

$$\frac{-a^{4}+a^{3}-2a^{3}+2a^{2}-12a+18}{3\times 2}$$

Combine like terms in $-a^{4}+a^{3}-2a^{3}+2a^{2}-12a+18$.

$$\frac{-a^{4}-a^{3}+2a^{2}-12a+18}{3\times 2}$$

Expand $3\times 2$.

$$\frac{-a^{4}-a^{3}+2a^{2}-12a+18}{6}$$

Expand

$-\frac{a^{4}}{6}-\frac{a^{3}}{6}+\frac{a^{2}}{3}-2a+3$

Short Solution Steps

Express $\frac{a}{3}\left(a+2\right)$ as a single fraction.

$$\frac{a\left(a+2\right)}{3}\times \frac{-a}{2}\left(a-1\right)-2a+3$$

Multiply $\frac{a\left(a+2\right)}{3}$ times $\frac{-a}{2}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{a\left(a+2\right)\left(-a\right)}{3\times 2}\left(a-1\right)-2a+3$$

Express $\frac{a\left(a+2\right)\left(-a\right)}{3\times 2}\left(a-1\right)$ as a single fraction.

$$\frac{a\left(a+2\right)\left(-a\right)\left(a-1\right)}{3\times 2}-2a+3$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $-2a+3$ times $\frac{3\times 2}{3\times 2}$.

$$\frac{a\left(a+2\right)\left(-a\right)\left(a-1\right)}{3\times 2}+\frac{\left(-2a+3\right)\times 3\times 2}{3\times 2}$$

Since $\frac{a\left(a+2\right)\left(-a\right)\left(a-1\right)}{3\times 2}$ and $\frac{\left(-2a+3\right)\times 3\times 2}{3\times 2}$ have the same denominator, add them by adding their numerators.

$$\frac{a\left(a+2\right)\left(-a\right)\left(a-1\right)+\left(-2a+3\right)\times 3\times 2}{3\times 2}$$

Do the multiplications in $a\left(a+2\right)\left(-a\right)\left(a-1\right)+\left(-2a+3\right)\times 3\times 2$.

$$\frac{-a^{4}+a^{3}-2a^{3}+2a^{2}-12a+18}{3\times 2}$$

Combine like terms in $-a^{4}+a^{3}-2a^{3}+2a^{2}-12a+18$.

$$\frac{-a^{4}-a^{3}+2a^{2}-12a+18}{3\times 2}$$

Expand $3\times 2$.

$$\frac{-a^{4}-a^{3}+2a^{2}-12a+18}{6}$$