Algebra

Problems related to equations, functions, polynomials, etc.

Problems in this category

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

We are asked to rationalize the numerator for each of the three given expressions. (i) $\frac{\sqrt{...

RadicalsRationalizationAlgebraic Manipulation
2025/5/10

The problem asks us to expand and simplify the expression $(a + 2)(a - 3) - 3(a - 5)$.

PolynomialsSimplificationExpandingCombining Like Terms
2025/5/10

The problem is to simplify the algebraic expression $5m - 2(x - 3m)$.

Algebraic ExpressionSimplificationCombining Like TermsDistribution
2025/5/10

The problem asks to: a) Express $\frac{\sqrt{3}+1}{\sqrt{3}-1} + \sqrt{3} - 1$ in the form $a + b\sq...

RationalizationRadicalsSimplificationAlgebraic Manipulation
2025/5/10

We are given a complex number $z = x + iy$, where $z$ is non-zero. We need to: a) Express $\frac{1}{...

Complex NumbersComplex ConjugateAbsolute Value of Complex NumbersProofs
2025/5/10