Combining Like Terms Practice worksheet for algebra students.

Sure! Let’s solve each expression by combining like terms.

> Like terms are terms that have the same variable raised to the same power. Constants (numbers with no variables) are also like terms with each other.

We’ll go row by row, left column first, then right column.

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🔹 Row 1:

Left: `5x + 2 + 3x`
→ Combine `5x + 3x = 8x`, and keep the constant `+2`
✔ Answer: `8x + 2`

Right: `3z + 6 + 4z + 9 + 8u`
→ Combine `3z + 4z = 7z`
→ Combine constants: `6 + 9 = 15`
→ `8u` has no like terms → leave as is
✔ Answer: `7z + 8u + 15`

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🔹 Row 2:

Left: `3 + 17x + 8`
→ Constants: `3 + 8 = 11`
→ `17x` has no like terms
✔ Answer: `17x + 11`

Right: `2x + 8z + 13u + 6z + 4u`
→ `8z + 6z = 14z`
→ `13u + 4u = 17u`
→ `2x` has no like terms
✔ Answer: `2x + 14z + 17u`

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🔹 Row 3:

Left: `19 + 6x + 2x`
→ `6x + 2x = 8x`
→ Constant: `19`
✔ Answer: `8x + 19`

Right: `14y + 13x + 12y + 19x + 4`
→ `14y + 12y = 26y`
→ `13x + 19x = 32x`
→ Constant: `4`
✔ Answer: `32x + 26y + 4`

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🔹 Row 4:

Left: `14x + 7 + 4`
→ Constants: `7 + 4 = 11`
→ `14x` alone
✔ Answer: `14x + 11`

Right: `5x + 18 - 13y + 12x + 8y`
→ `5x + 12x = 17x`
→ `-13y + 8y = -5y`
→ Constant: `18`
✔ Answer: `17x - 5y + 18`

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🔹 Row 5:

Left: `9x - 3 - 7x + 4`
→ `9x - 7x = 2x`
→ `-3 + 4 = +1`
✔ Answer: `2x + 1`

Right: `21v + 8 - 12v - 7 + 3t - t`
→ `21v - 12v = 9v`
→ `3t - t = 2t`
→ Constants: `8 - 7 = 1`
✔ Answer: `9v + 2t + 1`

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🔹 Row 6:

Left: `12x + 3x - 6 - 7f`
→ `12x + 3x = 15x`
→ `-6` and `-7f` remain (no like terms)
✔ Answer: `15x - 7f - 6`

Right: `3t + v - t + 7v`
→ `3t - t = 2t`
→ `v + 7v = 8v`
✔ Answer: `2t + 8v`

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🔹 Row 7:

Left: `14x + 7 - 3x`
→ `14x - 3x = 11x`
→ Constant: `7`
✔ Answer: `11x + 7`

Right: `-1 + 18x - 3y + x + 9y`
→ `18x + x = 19x`
→ `-3y + 9y = 6y`
→ Constant: `-1`
✔ Answer: `19x + 6y - 1`

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🔹 Row 8:

Left: `13z + 6u + 8x + 19 - u`
→ `6u - u = 5u`
→ `13z`, `8x`, `19` — no like terms for these
✔ Answer: `8x + 13z + 5u + 19`

Right: `4x + 5y + 5x + 10y`
→ `4x + 5x = 9x`
→ `5y + 10y = 15y`
✔ Answer: `9x + 15y`

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## ✔ Final Answers (organized in grid):

| Left Column | Right Column |
|--------------------------|----------------------------|
| `8x + 2` | `7z + 8u + 15` |
| `17x + 11` | `2x + 14z + 17u` |
| `8x + 19` | `32x + 26y + 4` |
| `14x + 11` | `17x - 5y + 18` |
| `2x + 1` | `9v + 2t + 1` |
| `15x - 7f - 6` | `2t + 8v` |
| `11x + 7` | `19x + 6y - 1` |
| `8x + 13z + 5u + 19` | `9x + 15y` |

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