7.EE.A.1 Worksheets | Printable 7th Grade Math Worksheets - Free Printable

Explanation:
We are asked to expand the brackets and then simplify each expression. That means:

1. Multiply the number outside the parentheses by each term inside.
2. Then combine like terms (terms with the same variable and exponent).

Let’s go through each problem carefully.

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Section A

1) $7(y + 4) + 8$
→ Expand: $7 \cdot y = 7y$, $7 \cdot 4 = 28$ → $7y + 28 + 8$
→ Simplify: $7y + 36$

2) $5(b + 2) + 4$
→ $5b + 10 + 4 = 5b + 14$

3) $3(a + 5) + 2a$
→ $3a + 15 + 2a = (3a + 2a) + 15 = 5a + 15$

4) $2(x + 6) + 7x$
→ $2x + 12 + 7x = (2x + 7x) + 12 = 9x + 12$

5) $4(9 + f) + 18f$
→ $36 + 4f + 18f = 36 + 22f$

6) $8(1 + 2g) + 5g$
→ $8 + 16g + 5g = 8 + 21g$

7) $9 + 3(c + 4)$
→ $9 + 3c + 12 = 3c + 21$

8) $11 + 5(6d + 5)$
→ $11 + 30d + 25 = 30d + 36$

9) $7x + 4(2x + 12)$
→ $7x + 8x + 48 = 15x + 48$

10) $12a + 9(5 + 2a)$
→ $12a + 45 + 18a = (12a + 18a) + 45 = 30a + 45$

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Section B

1) $6(3d - 1) + 8$
→ $18d - 6 + 8 = 18d + 2$

2) $5(6x - 2) + 2$
→ $30x - 10 + 2 = 30x - 8$

3) $7 - 3(8f + 6)$
→ $7 - (24f + 18) = 7 - 24f - 18 = -24f - 11$

4) $-9 - (4j + 5)$
→ $-9 - 4j - 5 = -4j - 14$

5) $8 - (1 - k)$
→ $8 - 1 + k = 7 + k$ or $k + 7$

6) $-2h - 4(6h - 1)$
→ $-2h - 24h + 4 = -26h + 4$

7) $5b(2b - 3) + 8$
→ First multiply: $5b \cdot 2b = 10b^2$, $5b \cdot (-3) = -15b$
→ So: $10b^2 - 15b + 8$

8) $7c(2c - 5) - 3$
→ $14c^2 - 35c - 3$

9) $9 - 2e(3 - 5e)$
→ Distribute: $-2e \cdot 3 = -6e$, $-2e \cdot (-5e) = +10e^2$
→ So: $9 - 6e + 10e^2$ → write in standard order: $10e^2 - 6e + 9$

10) $xy - x(y - 1)$
→ Expand second part: $x(y - 1) = xy - x$
→ So: $xy - (xy - x) = xy - xy + x = x$

Now double-check a few tricky ones:

- #3 Section B: $7 - 3(8f + 6) = 7 - 24f - 18 = -24f - 11$ ✔
- #5 Section B: $8 - (1 - k) = 8 - 1 + k = 7 + k$ ✔
- #10 Section B: $xy - x(y - 1) = xy - xy + x = x$ ✔
- #7 & #8: multiplication of variables — yes, $5b \cdot 2b = 10b^2$, etc. ✔

All steps check out.

Final Answer:
1) $7y + 36$
2) $5b + 14$
3) $5a + 15$
4) $9x + 12$
5) $36 + 22f$
6) $8 + 21g$
7) $3c + 21$
8) $30d + 36$
9) $15x + 48$
10) $30a + 45$
1) $18d + 2$
2) $30x - 8$
3) $-24f - 11$
4) $-4j - 14$
5) $k + 7$
6) $-26h + 4$
7) $10b^2 - 15b + 8$
8) $14c^2 - 35c - 3$
9) $10e^2 - 6e + 9$
10) $x$