Math Buddyv1.0

Algebra calculator with steps

Type or scan an algebra problem. MathBuddy simplifies, expands, factors or solves it and shows each step.

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What this page covers

  • Simplifying and expanding expressions with brackets and powers.
  • Factoring polynomials, including quadratics with a leading coefficient other than 1.
  • Solving linear and quadratic equations in one variable, and simplifying algebraic fractions.
  • Not covered here: inequalities (use Inequality calculator with steps) and several equations at once, which belong to a systems of equations page.

How to enter the problem

  • Type it as written, with a word such as Simplify, Factor or Solve in front. Powers and fractions render as you type.
  • Scan it. Fit the one problem in the frame.
  • Choose a photo. Several problems in one photo are solved as a list.
  • Then tap Solve.

Worked examples

Example 1

Problem

Factor 2x2+7x+3\displaystyle 2x^2 + 7x + 3.

Answer

Verified

The answer is

(2x+1)(x+3)(2x + 1)(x + 3)

Explanation

  1. Multiply the outer coefficients
    a⋅c=2⋅3=6a \cdot c = 2 \cdot 3 = 6
  2. Find two numbers
    66 and 11 multiply to 66 and add to 77.
  3. Split the middle term
    2x2+6x+x+32x^2 + 6x + x + 3.
  4. Factor in pairs
    2x(x+3)+1(x+3)2x(x + 3) + 1(x + 3).
  5. Take out the common bracket
    (2x+1)(x+3)(2x + 1)(x + 3).

Example 2

Problem

Solve x2−5x+6=0\displaystyle x^2 - 5x + 6 = 0.

Answer

Verified

The answer is

x=2,x=3x = 2, x = 3

Explanation

  1. Factor the left side
    Two numbers that multiply to 66 and add to −5-5 are −2-2 and −3-3
    (x−2)(x−3)=0(x - 2)(x - 3) = 0
  2. Set each factor to zero
    x−2=0x - 2 = 0 or x−3=0x - 3 = 0.
  3. Solve each
    x=2x = 2 or x=3x = 3.

Example 3

Problem

Simplify x2−16x2+2x−8\displaystyle \dfrac{x^2 - 16}{x^2 + 2x - 8}.

Answer

Verified

The answer is

x−4x−2\frac{x - 4}{x - 2}

Explanation

  1. Factor the numerator
    x2−16=(x−4)(x+4)x^2 - 16 = (x - 4)(x + 4), a difference of squares.
  2. Factor the denominator
    Two numbers that multiply to −8-8 and add to 22 are 44 and −2-2, so x2+2x−8=(x+4)(x−2)x^2 + 2x - 8 = (x + 4)(x - 2).
  3. Note the excluded values
    The original is undefined at x=−4x = -4 and x=2x = 2.
  4. Cancel the common factor
    Divide out (x+4)(x + 4), which leaves x−4x−2\frac{x - 4}{x - 2} for x≠−4x \neq -4.

Common mistakes

  • Squaring term by term. (x+3)2(x + 3)^2 is x2+6x+9x^2 + 6x + 9, not x2+9x^2 + 9.
  • Losing the minus sign in front of a bracket: −(x2−1)=−x2+1-(x^2 - 1) = -x^2 + 1.
  • Cancelling terms instead of factors. In x2−16x2+2x−8\frac{x^2 - 16}{x^2 + 2x - 8} the x2x^2 cannot be cancelled; factor first, then cancel a whole common factor.
  • Dividing both sides of x2=5xx^2 = 5x by xx, which loses the solution x=0x = 0.

Checks, assumptions and limits

  • Substitute a number. At x=2x = 2, (2+3)2−(1)(3)=22(2 + 3)^2 - (1)(3) = 22 and 6⋅2+10=226 \cdot 2 + 10 = 22.
  • Expand a factored answer to check it: (2x+1)(x+3)=2x2+7x+3(2x + 1)(x + 3) = 2x^2 + 7x + 3.
  • Cancelling a factor changes the domain: x−3x−2\frac{x - 3}{x - 2} equals the original fraction only for x≠−3x \neq -3 and x≠2x \neq 2.
  • MathBuddy can make mistakes. Double check important steps.

Related tasks

Frequently asked questions

Simplifying, expanding and factoring expressions, and solving equations in one variable. A word such as Simplify, Factor or Solve in front makes clear what you want done.

The solution comes as numbered steps, each with a short title, and ends with a Final Answer.

Ask a follow-up question in the same thread about that step. A typed follow-up needs sign-in.

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