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Example Solutions for Step-by-Step Algebra
Evaluation

Evaluate an expression at a point one step at a time:

evaluate x^2 + 2(x + 7) - 19 at x = 7
(x - 1)(x + 3)^2 + 7 where x = 2
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Equation Solving

Solve equations one step at a time:

solution to 2x - 3 = 1
x^2 + 5x + 6 = 0
solve (9^(x + 1)) - (28 (3^(x))) + 3 = 0 over the real numbers
solve sin(t) + cos(t) = 1
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Systems of Linear Equations

Solve linear systems with multiple methods:

x + y = 1, x - y = 3
solve 3x - y - z = 2, x + 2y - 3z = -12, 2x + y + 3z = 9
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Polynomials

Factor polynomials step by step:

factor x^3 - 8
factorization of x^4+4
factor x^3+2x^2+x+2

Expand polynomials using FOIL, the binomial theorem and other methods:

expanded form of (x + 3)^2
multiply out (x^2 + x)^4

Choose from multiple methods to complete the square:

complete the square x^2 + 2x + 3
complete the square x^2 + y^2 + 2x + 4y - 11 = 0
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Rational Functions

Simplify rational expressions with the steps provided:

simplify (1/a + 1/b) (a + b)
k/(k + 1) + 1/((k + 1) (k + 2))

Learn to rewrite a rational function using our step-by-step partial fraction decomposition:

partial fraction decomposition 1/(x^2 + 4x + 3)
1/(x^3 + 4x^2 + 5x + 2)
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Intercepts

Find axis intercepts one step at a time:

x intercepts of sin(x)
y intercept of x^2+1
intercepts of (x^2+2)(x^2-1)
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