Solve (x + y + z)(x + y - z) | 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

$$(x+y+z)(x+y-z)$$

Evaluate

$\left(x+y\right)^{2}-z^{2}$

Solution Steps

Apply the distributive property by multiplying each term of $x+y+z$ by each term of $x+y-z$.

$$x^{2}+xy-xz+yx+y^{2}-yz+zx+zy-z^{2}$$

Combine $xy$ and $yx$ to get $2xy$.

$$x^{2}+2xy-xz+y^{2}-yz+zx+zy-z^{2}$$

Combine $-xz$ and $zx$ to get $0$.

$$x^{2}+2xy+y^{2}-yz+zy-z^{2}$$

Combine $-yz$ and $zy$ to get $0$.

$$x^{2}+2xy+y^{2}-z^{2}$$

Expand

$x^{2}+2xy+y^{2}-z^{2}$

Solution Steps

Apply the distributive property by multiplying each term of $x+y+z$ by each term of $x+y-z$.

$$x^{2}+xy-xz+yx+y^{2}-yz+zx+zy-z^{2}$$

Combine $xy$ and $yx$ to get $2xy$.

$$x^{2}+2xy-xz+y^{2}-yz+zx+zy-z^{2}$$

Combine $-xz$ and $zx$ to get $0$.

$$x^{2}+2xy+y^{2}-yz+zy-z^{2}$$

Combine $-yz$ and $zy$ to get $0$.

$$x^{2}+2xy+y^{2}-z^{2}$$