Algebra

Problems related to equations, functions, polynomials, etc.

Problems in this category

The problem asks to express $(\sqrt[7]{4x})^3$ with a rational exponent. We are given that $x$ repre...

ExponentsRadicalsSimplification
2025/4/20

The problem asks to simplify the expression $(\sqrt{7} - 2\sqrt{3})^2$.

SimplificationExponentsRadicalsAlgebraic Manipulation
2025/4/20

The problem is to express the given expression in indices form. The expression is $\frac{1}{2(x+\Del...

ExponentsAlgebraic ManipulationVariables
2025/4/20

We are given a system of three linear equations with three variables, $x$, $y$, and $z$. The system ...

Linear EquationsSystems of EquationsGaussian EliminationVariable Elimination
2025/4/20

The problem is to solve the following system of equations: $x + y = 4$ $z - y = 3$ $2x + 2z = 3$

System of EquationsLinear EquationsSolution ExistenceContradiction
2025/4/20

We are given a system of three equations with three variables, $x$, $y$, and $z$. The equations are:...

Systems of EquationsLinear EquationsContradictionNo Solution
2025/4/20

The problem is to factor the polynomial $4x^3 - 8x^2 - 36x - 72$.

Polynomial FactorizationFactoring by GroupingDifference of Squares
2025/4/19

The problem has two parts. (a) Solve the inequality: $4 + \frac{3}{4}(x+2) \le \frac{3}{8}x + 1$. (b...

InequalitiesArea CalculationRectangleSquareAlgebraic Manipulation
2025/4/19

The problem states that a rectangle $PQRS$ has a square of side $x$ cut out from two of its corners....

GeometryAreaQuadratic EquationsProblem Solving
2025/4/19

The problem describes a rectangle PQRS with dimensions 20 cm and (10+10) cm = 20 cm. Two squares of ...

AreaQuadratic EquationsGeometric ShapesProblem SolvingError Analysis
2025/4/19