The image shows two algebraic problems: Problem 1: $(2x + 1) + (x - 5) + (3x - 2)$ Problem 2: $(x - y) + (y - z) + (z - x)$ We need to simplify both expressions.

AlgebraAlgebraic ExpressionsSimplificationCombining Like Terms
2025/5/13

1. Problem Description

The image shows two algebraic problems:
Problem 1: (2x+1)+(x5)+(3x2)(2x + 1) + (x - 5) + (3x - 2)
Problem 2: (xy)+(yz)+(zx)(x - y) + (y - z) + (z - x)
We need to simplify both expressions.

2. Solution Steps

Problem 1: (2x+1)+(x5)+(3x2)(2x + 1) + (x - 5) + (3x - 2)
Step 1: Remove the parentheses.
2x+1+x5+3x22x + 1 + x - 5 + 3x - 2
Step 2: Group like terms.
(2x+x+3x)+(152)(2x + x + 3x) + (1 - 5 - 2)
Step 3: Combine like terms.
6x66x - 6
Problem 2: (xy)+(yz)+(zx)(x - y) + (y - z) + (z - x)
Step 1: Remove the parentheses.
xy+yz+zxx - y + y - z + z - x
Step 2: Group like terms.
(xx)+(y+y)+(z+z)(x - x) + (-y + y) + (-z + z)
Step 3: Combine like terms.
0+0+0=00 + 0 + 0 = 0

3. Final Answer

Solution to Problem 1: 6x66x - 6
Solution to Problem 2: 00

Related problems in "Algebra"

Solve the inequality $x + 1 \ge 3x$.

InequalitiesLinear InequalitiesSolving Inequalities
2025/5/13

The problem asks to find the truth set for each of the given inequalities and illustrate the answer ...

InequalitiesLinear InequalitiesNumber Line
2025/5/13

The problem asks us to find the truth set (solution set) of the following inequalities and illustrat...

InequalitiesLinear InequalitiesSolution SetsNumber Line
2025/5/13

The problem asks us to find the next three terms in each of the given sequences.

SequencesArithmetic SequencesGeometric SequencesNumber Patterns
2025/5/13

The problem asks us to find the first five terms of two sequences given their general terms. i) $a_n...

SequencesSeriesArithmetic SequenceGeometric Sequence
2025/5/13

The problem is to solve a system of two linear equations with two variables, $x$ and $y$. The equati...

Linear EquationsSystems of EquationsSubstitutionNo SolutionParallel Lines
2025/5/13

The problem asks for the sum of a matrix $A$ and its negative $-A$. The matrix $A$ is given as: $A =...

Matrix AlgebraMatrix AdditionZero Matrix
2025/5/13

The problem provides a matrix $A$ and asks to find the element $a_{12}$.

MatricesMatrix Elements
2025/5/13

We have a set of algebra problems that involve simplifying expressions with additions and subtractio...

Simplifying ExpressionsPolynomialsCombining Like TermsAlgebraic Manipulation
2025/5/13

The problem is to simplify the expression $(2y^3 - 3y + 5) + (y^2 + 3y - 4)$. We need to combine lik...

PolynomialsSimplificationCombining Like Terms
2025/5/13