Algebraic expressions for simplifying like terms in a math worksheet.

Let's solve each expression in Part 1 by combining like terms. Like terms are terms that have the same variable raised to the same power. We'll add or subtract their coefficients.

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1. $ 4f + 9f + 9f + 2f + 9f $

Add all the coefficients of $ f $:

$$
4 + 9 + 9 + 2 + 9 = 33
$$

So, $ 33f $

✔ Answer: $ 33f $

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2. $ 4u + 7u + 8u - 8u + 4u $

Add the coefficients:

$$
4 + 7 + 8 - 8 + 4 = 15
$$

So, $ 15u $

✔ Answer: $ 15u $

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3. $ -8i + 7i - 7i + 7i $

Add the coefficients:

$$
-8 + 7 - 7 + 7 = -1
$$

So, $ -i $

✔ Answer: $ -i $

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4. $ 7l - 3l + 3l $

$$
7 - 3 + 3 = 7
$$

So, $ 7l $

✔ Answer: $ 7l $

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5. $ 8t + 5t - 7t - 4t - 8t $

Add the coefficients:

$$
8 + 5 - 7 - 4 - 8 = (13) - (19) = -6
$$

So, $ -6t $

✔ Answer: $ -6t $

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6. $ -5e + 4e + 9e + 2e - 3e $

Add the coefficients:

$$
-5 + 4 + 9 + 2 - 3 = (-5 - 3) + (4 + 9 + 2) = -8 + 15 = 7
$$

So, $ 7e $

✔ Answer: $ 7e $

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7. $ -6y - 7y + 9y + 4y $

Add the coefficients:

$$
-6 - 7 + 9 + 4 = (-13) + 13 = 0
$$

So, $ 0 $

✔ Answer: $ 0 $

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8. $ 4c + 6c + 4c $

$$
4 + 6 + 4 = 14
$$

So, $ 14c $

✔ Answer: $ 14c $

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9. $ 5j + 5j + 6j - 8j + 4j $

$$
5 + 5 + 6 - 8 + 4 = (16) - 8 = 8
$$

So, $ 8j $

✔ Answer: $ 8j $

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10. $ 2b - 10b - 4b + 9b + 2b $

$$
2 - 10 - 4 + 9 + 2 = (2 + 9 + 2) - (10 + 4) = 13 - 14 = -1
$$

So, $ -b $

✔ Answer: $ -b $

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11. $ 10t - 4t $

$$
10 - 4 = 6
$$

So, $ 6t $

✔ Answer: $ 6t $

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12. $ -5p + 3p $

$$
-5 + 3 = -2
$$

So, $ -2p $

✔ Answer: $ -2p $

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13. $ -9w - 6w $

$$
-9 - 6 = -15
$$

So, $ -15w $

✔ Answer: $ -15w $

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14. $ 8h + 9h - 10h $

$$
8 + 9 - 10 = 7
$$

So, $ 7h $

✔ Answer: $ 7h $

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✔ Final Answers:

1. $ 33f $
2. $ 15u $
3. $ -i $
4. $ 7l $
5. $ -6t $
6. $ 7e $
7. $ 0 $
8. $ 14c $
9. $ 8j $
10. $ -b $
11. $ 6t $
12. $ -2p $
13. $ -15w $
14. $ 7h $

Let me know if you'd like these explained step-by-step with visual grouping!