Combining Like Terms Calculator

Approach

Step 1

Step 1 - Set up the problem.

In this problem: The expression is \(3x + 2x - 5 + 7\), which is a sum of \(4\) terms.

Step 2

Step 2 - List the terms in groups, putting every term with the same variable part into one group and all the plain numbers into a group of their own.

In this problem: Reading the terms left to right, the variable parts are \(x\), \(x\), none, none. Matching them up gives \(2\) groups: the \(x\) terms with \(2\) of them, the plain numbers with \(2\) of them.

Step 3

Step 3 - Rewrite the expression with each group's terms next to each other, keeping every sign attached to the term in front of it.

In this problem: Reading left to right the order is already the \(x\) terms and the plain numbers, so every group's terms are side by side and nothing has to move. The expression is written out again unchanged as \(3x + 2x - 5 + 7\).

Step 4a

Step 4a - Take one group at a time and add or subtract the coefficients inside it, leaving the variable part unchanged.

In this problem: The \(x\) terms are \(3x + 2x\). Adding the coefficients gives \(3 + 2 = 5\), and the variable part stays \(x\), so the group becomes \(5x\).

Step 4b

Step 4b - Take one group at a time and add or subtract the coefficients inside it, leaving the variable part unchanged.

In this problem: The plain numbers are \(-5 + 7\). Adding them gives \(-5 + 7 = 2\).

Final Answer

Approach

Step 1

Step 1 - Set up the problem.

In this problem: The expression is \(4x^{2} + 3x - x^{2} + 5 - 2x\), which is a sum of \(5\) terms.

Step 2

Step 2 - List the terms in groups, putting every term with the same variable part into one group and all the plain numbers into a group of their own.

In this problem: Reading the terms left to right, the variable parts are \(x^{2}\), \(x\), \(x^{2}\), none, \(x\). Matching them up gives \(3\) groups: the \(x^{2}\) terms with \(2\) of them, the \(x\) terms with \(2\) of them, the plain numbers with \(1\) of them.

Step 3

Step 3 - Rewrite the expression with each group's terms next to each other, keeping every sign attached to the term in front of it.

In this problem: The groups are not side by side yet, so the terms are written out again in the order the \(x^{2}\) terms, the \(x\) terms and the plain numbers, each one keeping the sign in front of it, which gives \(4x^{2} - x^{2} + 3x - 2x + 5\).

Step 4a

Step 4a - Take one group at a time and add or subtract the coefficients inside it, leaving the variable part unchanged.

In this problem: The \(x^{2}\) terms are \(4x^{2} - x^{2}\). Adding the coefficients gives \(4 - 1 = 3\), and the variable part stays \(x^{2}\), so the group becomes \(3x^{2}\).

Step 4b

Step 4b - Take one group at a time and add or subtract the coefficients inside it, leaving the variable part unchanged.

In this problem: The \(x\) terms are \(3x - 2x\). Adding the coefficients gives \(3 - 2 = 1\), and the variable part stays \(x\), so the group becomes \(x\). The remaining \(5\) has nothing to pair with, so it comes down unchanged.

Final Answer