Solve 4 ( a-3 3( a ) a 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

$$2 ( a - 3 ) ^ { 2 } - 3 ( a - 4 ) ( a + 3 )$$

Evaluate

$54-9a-a^{2}$

Solution Steps

Use binomial theorem $\left(p-q\right)^{2}=p^{2}-2pq+q^{2}$ to expand $\left(a-3\right)^{2}$.

$$2\left(a^{2}-6a+9\right)-3\left(a-4\right)\left(a+3\right)$$

Use the distributive property to multiply $2$ by $a^{2}-6a+9$.

$$2a^{2}-12a+18-3\left(a-4\right)\left(a+3\right)$$

Use the distributive property to multiply $-3$ by $a-4$.

$$2a^{2}-12a+18+\left(-3a+12\right)\left(a+3\right)$$

Use the distributive property to multiply $-3a+12$ by $a+3$ and combine like terms.

$$2a^{2}-12a+18-3a^{2}+3a+36$$

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

$$-a^{2}-12a+18+3a+36$$

Combine $-12a$ and $3a$ to get $-9a$.

$$-a^{2}-9a+18+36$$

Add $18$ and $36$ to get $54$.

$$-a^{2}-9a+54$$

Expand

$54-9a-a^{2}$

Solution Steps

Use binomial theorem $\left(p-q\right)^{2}=p^{2}-2pq+q^{2}$ to expand $\left(a-3\right)^{2}$.

$$2\left(a^{2}-6a+9\right)-3\left(a-4\right)\left(a+3\right)$$

Use the distributive property to multiply $2$ by $a^{2}-6a+9$.

$$2a^{2}-12a+18-3\left(a-4\right)\left(a+3\right)$$

Use the distributive property to multiply $-3$ by $a-4$.

$$2a^{2}-12a+18+\left(-3a+12\right)\left(a+3\right)$$

Use the distributive property to multiply $-3a+12$ by $a+3$ and combine like terms.

$$2a^{2}-12a+18-3a^{2}+3a+36$$

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

$$-a^{2}-12a+18+3a+36$$

Combine $-12a$ and $3a$ to get $-9a$.

$$-a^{2}-9a+18+36$$

Add $18$ and $36$ to get $54$.

$$-a^{2}-9a+54$$