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