Solve n-; (2x - 3y) ^ 2 + 2(2x - 3y) + (2x - 3y) ^ 2 | 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

$$n-; (2x-3y)^{2}+2(2x-3y)+(2x-3y)^{2}$$

Evaluate

$\left(2x-3y\right)^{2}+6x-13y$

Solution Steps

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

$$4x^{2}-12xy+9y^{2}+2\left(2x-5y\right)+2x-3y$$

Use the distributive property to multiply $2$ by $2x-5y$.

$$4x^{2}-12xy+9y^{2}+4x-10y+2x-3y$$

Combine $4x$ and $2x$ to get $6x$.

$$4x^{2}-12xy+9y^{2}+6x-10y-3y$$

Combine $-10y$ and $-3y$ to get $-13y$.

$$4x^{2}-12xy+9y^{2}+6x-13y$$

Expand

$4x^{2}-12xy+6x+9y^{2}-13y$

Solution Steps

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

$$4x^{2}-12xy+9y^{2}+2\left(2x-5y\right)+2x-3y$$

Use the distributive property to multiply $2$ by $2x-5y$.

$$4x^{2}-12xy+9y^{2}+4x-10y+2x-3y$$

Combine $4x$ and $2x$ to get $6x$.

$$4x^{2}-12xy+9y^{2}+6x-10y-3y$$

Combine $-10y$ and $-3y$ to get $-13y$.

$$4x^{2}-12xy+9y^{2}+6x-13y$$