Solve (4x-+3y)^(2)-(4x-3y)^(2)-48xy | 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

$${ \left(4x-+3y \right) }^{ 2 } - { \left(4x-3y \right) }^{ 2 } -48xy$$

Evaluate

$-48xy$

Solution Steps

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(4x-3y\right)^{2}$.

$$16x^{2}-24xy+9y^{2}-\left(4x-3y\right)^{2}-48xy$$

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(4x-3y\right)^{2}$.

$$16x^{2}-24xy+9y^{2}-\left(16x^{2}-24xy+9y^{2}\right)-48xy$$

To find the opposite of $16x^{2}-24xy+9y^{2}$, find the opposite of each term.

$$16x^{2}-24xy+9y^{2}-16x^{2}+24xy-9y^{2}-48xy$$

Combine $16x^{2}$ and $-16x^{2}$ to get $0$.

$$-24xy+9y^{2}+24xy-9y^{2}-48xy$$

Combine $-24xy$ and $24xy$ to get $0$.

$$9y^{2}-9y^{2}-48xy$$

Combine $9y^{2}$ and $-9y^{2}$ to get $0$.

$$0-48xy$$

Anything plus zero gives itself.

$$-48xy$$

Expand

$-48xy$

Solution Steps

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(4x-3y\right)^{2}$.

$$16x^{2}-24xy+9y^{2}-\left(4x-3y\right)^{2}-48xy$$

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(4x-3y\right)^{2}$.

$$16x^{2}-24xy+9y^{2}-\left(16x^{2}-24xy+9y^{2}\right)-48xy$$

To find the opposite of $16x^{2}-24xy+9y^{2}$, find the opposite of each term.

$$16x^{2}-24xy+9y^{2}-16x^{2}+24xy-9y^{2}-48xy$$

Combine $16x^{2}$ and $-16x^{2}$ to get $0$.

$$-24xy+9y^{2}+24xy-9y^{2}-48xy$$

Combine $-24xy$ and $24xy$ to get $0$.

$$9y^{2}-9y^{2}-48xy$$

Combine $9y^{2}$ and $-9y^{2}$ to get $0$.

$$0-48xy$$

Anything plus zero gives itself.

$$-48xy$$