Algebra topic hub
Understand equality, inequalities, roots, powers, polynomials, sequences, and equation-solving notation.
Topic overview
Connect common algebra symbols to formulas and interactive tools, with explicit domains and verification steps.
Recommended order
Identify the relation and operands
Check domain restrictions
Apply a formula or transformation
Substitute the result back
Match the page to your intent
Popular searches
Avoid these errors
Interactive workflow
Step-by-step explanations
Comparisons
Know when to use ≈, =, ≡, and other relation symbols.
Read guideScientific writing
Compare normalized scientific notation with engineering notation and choose powers of ten that match technical units.
Read guideAlgebra
Choose factoring, completing the square, or the quadratic formula, then verify every root in the original quadratic equation.
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Factor quadratic trinomials by identifying factor pairs, checking signs, and multiplying the factors back to the original polynomial.
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Solve exponential equations by matching bases or taking logarithms, then check domain and substitute the result.
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Solve one-variable linear equations by simplifying both sides, isolating the variable, and checking the result in the original equation.
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Solve one-variable linear inequalities, reverse the inequality when dividing by a negative, and represent the solution on a number line.
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Solve two-variable linear systems using elimination or substitution, classify the intersection, and check both original equations.
Read guideReviewed notation
\sqrt{x}\neq\approx\circledequal\sum\bumpeq\Bumpeq\ominusVariables and assumptions
Algebra
x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}Finds the roots of a quadratic equation ax² + bx + c = 0 when a is nonzero.
Open formulaAlgebra
a_n=a_1+(n-1)dFinds the nth term of a sequence with a constant difference.
Open formulaAlgebra
a_n=a_1r^{n-1}Finds the nth term of a sequence with a constant ratio.
Open formulaAlgebra
(a+b)^n=\sum_{k=0}^{n}\binom{n}{k}a^{n-k}b^kExpands a nonnegative integer power of a binomial.
Open formulaAlgebra
S_n=\frac n2(a_1+a_n)Computes the sum of the first n terms of an arithmetic sequence.
Open formulaLinear Algebra
\det\begin{pmatrix}a&b\\c&d\end{pmatrix}=ad-bcCalculates the determinant of a two-by-two matrix.
Open formulaExplore nearby topics
Identify the relation and operands
Read algebra notation Use common formulas Verify equation solutions
Dividing by a possibly zero expression