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Example math equations:

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Pre AlgebraAlgebraPre CalculusCalculusLinear Algebra
Arithmetic
Simplify :
(6+3)⋅(10−7)(6+3)\cdot (10-7)
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Negative numbers
Simplify :
−49−3−6\frac{-4}{9}-\frac{3}{-6}
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Linear inequalities 1
Solve for x:
x−4≥−6x-4\ge-6
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Powers and roots 1
Simplify :
36\sqrt{36}
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Fraction
Simplify :
310+610\frac{3}{10}+\frac{6}{10}
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Linear equations 1
Solve for x:
4x=34x=3
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Linear equations 2
Solve for x:
2x3+5=x−92\frac{2x}{3}+5= x-\frac{9}{2}
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Systems of equations 1
Solve the system :
5x−3y=64x−5y=12\begin{array} {l} {5x-3y = 6} \\ {4x-5y = 12} \end{array}
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Powers and roots 2
Expand for x:
(x+7)2(x+7)^2
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Polynomials and quadratic expressions
Factor for x:
9x2−6x+19x^2-6x+1
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Linear inequalities 2
Solve for x:
x+42≤7x5\frac{x+4}{2}\le\frac{7x}{5}
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Quadratic equations
Solve for x:
x2−x−1=0x^2-x-1=0
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Adding matrices
Simplify :
[1534]+[7124]+[2381]\left[ \begin{array}{cc} {1} & {5} \\ {3} & {4} \end{array} \right] + \left[ \begin{array}{cc} {7} & {1} \\ {2} & {4} \end{array} \right] + \left[ \begin{array}{cc} {2} & {3} \\ {8} & {1} \end{array} \right]
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Multiplying matrices
Simplify :
[3201]⋅[5268]\left[ \begin{array}{cc} {3} & {2} \\ {0} & {1} \end{array} \right] \cdot \left[ \begin{array}{cc} {5} & {2} \\ {6} & {8} \end{array} \right]
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Matrix inverses and determinants
Calculate the determinant :
[25−50]\left[ \begin{array}{cc} {2} & {5} \\ {-5} & {0} \end{array} \right]
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Systems of equations 2
Solve the system :
5x−3y=64x−5y=12\begin{array} {l} {5x-3y = 6} \\ {4x-5y = 12} \end{array}
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Exponential and logarithmic functions
Solve for x:
3e3x⋅e−2x+5=23e^{3x} \cdot e^{-2x+5}=2
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Systems of equations 2
Solve the system :
29⋅x−5y=1945⋅x+3y=2\begin{array} {l} {\frac{2}{9} \cdot x-5y = \frac{1}{9}} \\ {\frac{4}{5}\cdot x+3y = 2} \end{array}
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Fundamental derivatives
Find the derivative :
cos⁡(x)\cos(x)
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Curve sketching
Analyze the function for x:
f(x)=x3−xf(x)=x^3-x
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Fundamental integrals
Find the integral :
x2x^2
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General derivatives
Find the derivative :
tan⁡(x)+x\tan(x)+\sqrt{x}
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General integrals
Find the integral :
x⋅exx \cdot e^x
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Fundamental derivatives
Find the derivative :
ln⁡(x)\ln(x)
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Determinants
Calculate the determinant :
[−3782]\left[ \begin{array}{cc} {-3} & {7} \\ {8} & {2} \end{array} \right]
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Characteristic polynomial
Find the characteristic polynomial :
[12−24]\left[ \begin{array}{cc} {1} & {2} \\ {-2} & {4} \end{array} \right]
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Eigenvalues
Find the eigenvalues :
[−1341]\left[ \begin{array}{cc} {-1} & {3} \\ {4} & {1} \end{array} \right]
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Matrix operations
Simplify :
[0−1−21]⋅[1734]\left[ \begin{array}{cc} {0} & {-1} \\ {-2} & {1} \end{array} \right] \cdot \left[ \begin{array}{cc} {1} & {7} \\ {3} & {4} \end{array} \right]
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Inverse matrices
Find the inverse matrix :
[3−2314−232−5]\left[ \begin{array}{ccc} {3} & {-2} & {3} \\ {1} & {4} & {-2} \\ {3} & {2} & {-5} \end{array} \right]
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Matrix operations
Simplify :
[21−52−3−4−317]+[41−43−5−6271]\left[ \begin{array}{ccc} {2} & {1} & {-5} \\ {2} & {-3} & {-4} \\ {-3} & {1} & {7} \end{array} \right]+ \left[ \begin{array}{ccc} {4} & {1} & {-4} \\ {3} & {-5} & {-6} \\ {2} & {7} & {1} \end{array} \right]
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