Algebra

Problems related to equations, functions, polynomials, etc.

Problems in this category

We are asked to expand the expression $y = (-2x^4 - 3)(-2x^2 + 1)$.

Polynomial ExpansionDistributive PropertyFOIL method

We are given the function $f(x) = x^2(-3x^2 - 2)$ and need to simplify it by expanding the expressio...

PolynomialsSimplificationExponents

We are given a system of two equations: $x - y = -1$ $y = x^2 + 1$ We need to solve for $x$ and $y$.

Systems of EquationsSubstitutionQuadratic EquationsSolving Equations

We are given a system of two equations: $x^2 + y^2 = 40$ $x^2 - y^2 = 10$ We are asked to solve for ...

Systems of EquationsQuadratic EquationsSolving Equations

We are given a system of two equations with two variables, $x$ and $y$. The equations are: $x^2 + y^...

Systems of EquationsSolving EquationsVariablesExponents

The problem asks to solve the inequality $4 + \frac{3}{4}(x+2) \le \frac{3}{8}x + 1$.

InequalitiesLinear InequalitiesSolving Inequalities

We are asked to rationalize the denominator and simplify the given expressions: a. $\frac{3}{\sqrt{2...

RationalizationRadicalsSimplificationAlgebraic Manipulation

We are asked to factor the expression $\sin^2 \theta - \sin \theta - 12$.

TrigonometryFactoringQuadratic Equations

The problem requires us to simplify several complex number expressions, find the quotient of complex...

Complex NumbersComplex Number ArithmeticComplex ConjugateAbsolute ValueSquare Root

The problem asks us to simplify the algebraic expression $4b - 3(4 - 2b)$.

Algebraic simplificationLinear expressionsDistributionCombining like terms

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