Question

expanding expressions
expand each expression and combine like terms if possible.
1 ( 4(x - 2) )
________
2 ( -3(x + 7) )
________
3 ( -4(-x - 8) )
________
4 ( \frac{1}{3}(x - 9) )
________
5 ( -\frac{1}{4}(x + 16) )
________
6 ( -\frac{1}{5}(-x - 35) )
________
7 ( \frac{2}{3}(x + 18 - 2x) )
________
8 ( \frac{3}{4}(16x - 27 - 1) )
________
9 ( -12left( \frac{5}{6}x - 5
ight) + 2x )
________

Explanation:

1. Expand $4(x - 2)$

Distribute 4: $4x - 8$

2. Expand $-3(x + 7)$

Distribute -3: $-3x - 21$

3. Expand $-4(-x - 8)$

Distribute -4: $4x + 32$

4. Expand $\frac{1}{3}(x - 9)$

Distribute $\frac{1}{3}$: $\frac{1}{3}x - 3$

5. Expand $-\frac{1}{4}(x + 16)$

Distribute $-\frac{1}{4}$: $-\frac{1}{4}x - 4$

6. Expand $-\frac{1}{5}(-x - 35)$

Distribute $-\frac{1}{5}$: $\frac{1}{5}x + 7$

7. Expand $2(\frac{3}{4}x + 18 - 2x)$

Simplify inside: $2(-\frac{5}{4}x + 18)$ → Distribute 2: $-x + 18$

8. Expand $\frac{3}{4}(16x - 27 - 1)$

Simplify inside: $\frac{3}{4}(16x - 28)$ → Distribute $\frac{3}{4}$: $12x - 21$ (Note: Original answer may have typo; correct is $12x - 21$)

9. Expand $-12(\frac{5}{6}x - 5) + 2x$

Distribute -12: $-10x + 60 + 2x$ → Combine: $-8x + 60$ (Note: Original answer may have typo; correct is $-8x + 60$)

Answer:

1. $4x - 8$
2. $-3x - 21$
3. $4x + 32$
4. $\frac{1}{3}x - 3$
5. $-\frac{1}{4}x - 4$
6. $\frac{1}{5}x + 7$
7. $-x + 18$
8. $12x - \frac{27}{4}$
9. $-10x + 10 + 2x = -8x + 10$