Algebra
Problems related to equations, functions, polynomials, etc.
Problems in this category
The problem defines a piecewise function $f(x)$ as follows: $f(x) = x^2 - 6$ if $x < 0$ $f(x) = 10 -...
Piecewise FunctionsGraphingQuadratic EquationsLinear EquationsSolving Equations
2025/5/11
We are given the complex numbers $z_1 = -1 + i\sqrt{3}$ and $z_2 = 1 - i\sqrt{3}$. We need to comput...
Complex NumbersComplex Number ArithmeticTrigonometric FormModulusArgument
2025/5/11
The problem asks us to simplify the given expression: $a^3 + a^2 - (b^2 + 1)a + b^2 - 1$.
Polynomial SimplificationFactoringDifference of Squares
2025/5/11
The problem is to evaluate the expression $2^{34} - 2^{33}$.
ExponentsFactorizationApproximationCalculation
2025/5/11
The problem asks us to factor the expression $x^4 + x^2y^2 + y^4$.
Polynomial FactorizationAlgebraic ManipulationDifference of Squares
2025/5/11
The problem asks to simplify the expression $bc(b - c) + ca(c - a) + ab(a - b)$.
Polynomial simplificationFactorizationAlgebraic manipulation
2025/5/11
Given vectors $a = (1, 3)$ and $b = (4, -2)$, we need to express the given vectors $c$ and $d$ in th...
VectorsLinear CombinationsSystems of EquationsLinear Algebra
2025/5/11
The problem asks whether the provided graph represents a function and its inverse. The graph shows t...
FunctionsInverse FunctionsGraphsExponentialsLogarithmsCoordinate Geometry
2025/5/10
The problem asks to simplify the expression $4x^2 - 3x(2x - 5)$.
Polynomial simplificationAlgebraic manipulationExpanding expressions
2025/5/10
The problem consists of two parts. First, we need to find an expression for the amount of money Mary...
Algebraic ExpressionsSystems of EquationsLinear EquationsVariable SubstitutionSimplification
2025/5/10