Algebraic Expressions (Addition & Subtraction) online worksheet ... - Free Printable

Let's solve each problem step by step.

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Problem 1: Add \((7j^3 - 2) + (5j^3 - j - 3)\)

Solution:
1. Combine like terms:
- \(7j^3 + 5j^3 = 12j^3\)
- \(-j\) remains as \(-j\)
- \(-2 - 3 = -5\)

So, the expression becomes:
\[ 12j^3 - j - 5 \]

Answer: \(\boxed{12j^3 - j - 5}\)

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Problem 2: Add \((-5x^2 - x + 4) + (-3x^2 - 5x + 2)\)

Solution:
1. Combine like terms:
- \(-5x^2 - 3x^2 = -8x^2\)
- \(-x - 5x = -6x\)
- \(4 + 2 = 6\)

So, the expression becomes:
\[ -8x^2 - 6x + 6 \]

Answer: \(\boxed{-8x^2 - 6x + 6}\)

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Problem 3: Subtract \(13x + 12y - 5\) from \(27x + 5y - 43\)

Solution:
1. Write the subtraction as:
\[ (27x + 5y - 43) - (13x + 12y - 5) \]
2. Distribute the negative sign:
\[ 27x + 5y - 43 - 13x - 12y + 5 \]
3. Combine like terms:
- \(27x - 13x = 14x\)
- \(5y - 12y = -7y\)
- \(-43 + 5 = -38\)

So, the expression becomes:
\[ 14x - 7y - 38 \]

Answer: \(\boxed{14x - 7y - 38}\)

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Problem 4: Simplify \((x + y - z) + (3x - 5y + 7z) - (14x + 7y - 6z)\)

Solution:
1. Combine all terms:
\[ (x + y - z) + (3x - 5y + 7z) - (14x + 7y - 6z) \]
2. Distribute the negative sign in the last term:
\[ x + y - z + 3x - 5y + 7z - 14x - 7y + 6z \]
3. Combine like terms:
- \(x + 3x - 14x = -10x\)
- \(y - 5y - 7y = -11y\)
- \(-z + 7z + 6z = 12z\)

So, the expression becomes:
\[ -10x - 11y + 12z \]

Answer: \(\boxed{-10x - 11y + 12z}\)

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Problem 5: Find \(x^2 - [3x + [2x - (x^2 - 1)] + 2]\)

Solution:
1. Simplify the innermost expression:
\[ 2x - (x^2 - 1) = 2x - x^2 + 1 \]
2. Substitute back:
\[ 3x + [2x - x^2 + 1] = 3x + 2x - x^2 + 1 = 5x - x^2 + 1 \]
3. Substitute into the outer expression:
\[ x^2 - [5x - x^2 + 1 + 2] = x^2 - [5x - x^2 + 3] \]
4. Distribute the negative sign:
\[ x^2 - 5x + x^2 - 3 \]
5. Combine like terms:
- \(x^2 + x^2 = 2x^2\)
- \(-5x\) remains as \(-5x\)
- \(-3\) remains as \(-3\)

So, the expression becomes:
\[ 2x^2 - 5x - 3 \]

Answer: \(\boxed{2x^2 - 5x - 3}\)

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Problem 6: Solve for \(n + (m + 1) + (n + 2) + (m + 3) + (n + 4) + (m + 5)\)

Solution:
1. Combine like terms:
- \(n + n + n = 3n\)
- \(m + m + m = 3m\)
- \(1 + 2 + 3 + 4 + 5 = 15\)

So, the expression becomes:
\[ 3m + 3n + 15 \]

Answer: \(\boxed{3m + 3n + 15}\)

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Problem 7: Subtract \(3x^2 - 6x - 4\) from \(5 + x - 2x^2\)

Solution:
1. Write the subtraction as:
\[ (5 + x - 2x^2) - (3x^2 - 6x - 4) \]
2. Distribute the negative sign:
\[ 5 + x - 2x^2 - 3x^2 + 6x + 4 \]
3. Combine like terms:
- \(-2x^2 - 3x^2 = -5x^2\)
- \(x + 6x = 7x\)
- \(5 + 4 = 9\)

So, the expression becomes:
\[ -5x^2 + 7x + 9 \]

Answer: \(\boxed{-5x^2 + 7x + 9}\)

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Problem 8: Add \(7abc, -5abc, 9abc\), and \(-8abc\)

Solution:
1. Combine like terms:
\[ 7abc - 5abc + 9abc - 8abc \]
2. Simplify:
\[ (7 - 5 + 9 - 8)abc = 3abc \]

So, the expression becomes:
\[ 3abc \]

Answer: \(\boxed{3abc}\)

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Problem 9: Add \(2x^2 - 3x + 1\) to the sum of \(3x^2 - 2x\) and \(3x + 7\)

Solution:
1. First, find the sum of \(3x^2 - 2x\) and \(3x + 7\):
\[ (3x^2 - 2x) + (3x + 7) = 3x^2 - 2x + 3x + 7 = 3x^2 + x + 7 \]
2. Now, add \(2x^2 - 3x + 1\) to this result:
\[ (2x^2 - 3x + 1) + (3x^2 + x + 7) \]
3. Combine like terms:
- \(2x^2 + 3x^2 = 5x^2\)
- \(-3x + x = -2x\)
- \(1 + 7 = 8\)

So, the expression becomes:
\[ 5x^2 - 2x + 8 \]

Answer: \(\boxed{5x^2 - 2x + 8}\)

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Problem 10: Subtract \(-x^2 - 3z\) from \(5x^2 - y + z + 7\)

Solution:
1. Write the subtraction as:
\[ (5x^2 - y + z + 7) - (-x^2 - 3z) \]
2. Distribute the negative sign:
\[ 5x^2 - y + z + 7 + x^2 + 3z \]
3. Combine like terms:
- \(5x^2 + x^2 = 6x^2\)
- \(-y\) remains as \(-y\)
- \(z + 3z = 4z\)
- \(7\) remains as \(7\)

So, the expression becomes:
\[ 6x^2 - y + 4z + 7 \]

Answer: \(\boxed{6x^2 - y + 4z + 7}\)

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Final Answers:

1. \(\boxed{12j^3 - j - 5}\)
2. \(\boxed{-8x^2 - 6x + 6}\)
3. \(\boxed{14x - 7y - 38}\)
4. \(\boxed{-10x - 11y + 12z}\)
5. \(\boxed{2x^2 - 5x - 3}\)
6. \(\boxed{3m + 3n + 15}\)
7. \(\boxed{-5x^2 + 7x + 9}\)
8. \(\boxed{3abc}\)
9. \(\boxed{5x^2 - 2x + 8}\)
10. \(\boxed{6x^2 - y + 4z + 7}\)