Evaluating Algebraic Expressions Calculator

Published on: October 27, 2024
Final Answer: Free • Full Steps: Plus

This Evaluating Algebraic Expressions Calculator works out what an expression is worth once a value is given for every letter in it, and shows the working at every step. Each letter is swapped for its value inside brackets, so a negative sign is never lost along the way. The terms are then worked out one at a time, powers before multiplying, and the results are added and subtracted from left to right. Following the same pattern every time is what makes evaluating easy to picture, check, and repeat on your own.

Step-by-step method

  1. Set up the problem.
  2. Replace every variable with the value given for it, wrapping a value in brackets so a negative sign is not lost.
  3. Work out each term on its own, dealing with any power before multiplying.
  4. Add and subtract the results from left to right.
See Example 1 Hide Example 1

Problem

\(2x + 3y, \;\; x = 3, \; y = 5\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Replace every variable with the value given for it, wrapping a value in brackets so a negative sign is not lost.
  3. Work out each term on its own, dealing with any power before multiplying.
  4. Add and subtract the results from left to right.

Step 1

Step 1 - Set up the problem.

In this problem: The expression is \(2x + 3y\) and the values given are \(x = 3, \; y = 5\).

\(2x + 3y, \;\; x = 3, \; y = 5\)

Step 2

Step 2 - Replace every variable with the value given for it, wrapping a value in brackets so a negative sign is not lost.

In this problem: Every letter is swapped for its value, so \(x\) becomes \(\left(3\right)\) and \(y\) becomes \(\left(5\right)\), which turns \(2x + 3y\) into \(2\left(3\right) + 3\left(5\right)\).

\(2x + 3y = 2\left(3\right) + 3\left(5\right)\)

Step 3

Step 3 - Work out each term on its own, dealing with any power before multiplying.

In this problem: There are \(2\) terms holding a value to work out, and each one is finished before the next is started.

\(2\left(3\right) + 3\left(5\right)\)

Step 3a

Step 3a - Work out each term on its own, dealing with any power before multiplying.

In this problem: Multiplying the term out gives \(2 \cdot 3 = 6\).

\(6 + 3\left(5\right)\)

Step 3b

Step 3b - Work out each term on its own, dealing with any power before multiplying.

In this problem: Multiplying the term out gives \(3 \cdot 5 = 15\).

\(6 + 15\)

Step 4

Step 4 - Add and subtract the results from left to right.

In this problem: Working left to right through \(6 + 15\) gives \(21\).

\(6 + 15 = 21\)

Final Answer

\(2x + 3y = 21\)
See Example 2 Hide Example 2

Problem

\(5a^{2} - 2b, \;\; a = -1, \; b = 4\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Replace every variable with the value given for it, wrapping a value in brackets so a negative sign is not lost.
  3. Work out each term on its own, dealing with any power before multiplying.
  4. Add and subtract the results from left to right.

Step 1

Step 1 - Set up the problem.

In this problem: The expression is \(5a^{2} - 2b\) and the values given are \(a = -1, \; b = 4\).

\(5a^{2} - 2b, \;\; a = -1, \; b = 4\)

Step 2

Step 2 - Replace every variable with the value given for it, wrapping a value in brackets so a negative sign is not lost.

In this problem: Every letter is swapped for its value, so \(a\) becomes \(\left(-1\right)\) and \(b\) becomes \(\left(4\right)\), which turns \(5a^{2} - 2b\) into \(5\left(-1\right)^{2} - 2\left(4\right)\).

\(5a^{2} - 2b = 5\left(-1\right)^{2} - 2\left(4\right)\)

Step 3

Step 3 - Work out each term on its own, dealing with any power before multiplying.

In this problem: There are \(2\) terms holding a value to work out, and each one is finished before the next is started.

\(5\left(-1\right)^{2} - 2\left(4\right)\)

Step 3a

Step 3a - Work out each term on its own, dealing with any power before multiplying.

In this problem: The power is worked out first: \(\left(-1\right)^{2} = 1\). Multiplying what is left gives \(5 \cdot 1 = 5\).

\(5 - 2\left(4\right)\)

Step 3b

Step 3b - Work out each term on its own, dealing with any power before multiplying.

In this problem: Multiplying the term out gives \(2 \cdot 4 = 8\).

\(5 - 8\)

Step 4

Step 4 - Add and subtract the results from left to right.

In this problem: Working left to right through \(5 - 8\) gives \(-3\).

\(5 - 8 = -3\)

Final Answer

\(5a^{2} - 2b = -3\)

Example Problems

Click one to load it into the box and solve it.