Step 1: | Remove all parentheses. I suggest writing the problem vertically rather than horizontally because it makes the next step must easier. When adding, distribute the positive (or addition) sign, which does not change any of the signs. When subtracting, distribute the negative (or subtraction) sign, which changes each sign after the subtraction sign. |
Step 2: | Combine like terms. This step is much easier if things are written vertically because like terms are written above one another. Remember that to combine like terms the variable and the power of each variable must be exactly the same. |
Example 1 – Simplify: (3x^{3} – 5x + 9) + (6x^{3} + 8x – 7)
Step 1: Remove all parentheses. | |
Step 2: Combine like terms. |
Example 2 – Simplify: (–3x^{2} + 9xy – 5y^{2}) – (4x^{2} + 7xy – 8y^{2})
Step 1: Remove all parentheses. | |
Step 2: Combine like terms. |
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Example 3 – Simplify: (5x^{3} – 7x^{2} – 8) – (4x^{2} + 5x – 6)
Step 1: Remove all parentheses. In this case, notice I left a blank in the first row to help align the like terms, making them easier to combine in the next step. | |
Step 2: Combine like terms. |
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Example 4 – Add 4x^{3} – 9x + 3 and 5x^{2} – 4x + 7.
Step 1: Write the problem using parentheses. We should use parentheses in this type of problem because we are adding groups of terms. | |
Step 2: Remove all parentheses. In this case, notice I left a blank in the first row to help align the like terms, making them easier to combine in the next step. | |
Step 3: Combine like terms. |
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Example 5 – Subtract 4x^{2} – 7x + 5 from 3x^{2} – 2x + 6.
Step 1: Write the problem using parentheses. We should use parentheses in this type of problem because we are subtracting groups of terms. | |
Step 2: Remove all parentheses. | |
Step 3: Combine like terms. |