Question

simplifying expressions
name ____
simplify each expression and match it to the simplified version.
$3a+4b-2a+3-7$
$3a+2(4a-b)$
$2(4a+b)+3(a-3b)$
$4(2a-2)+4(a-b)$
$7(a-2b+2)+7b$
$3(a+2)-4(b+3)+2(a+1)$
$2(b-4)-3(a+2b+3)$
$-3(a-b)-7(2a+b)$
$2(2a-b)-4(a+3b)$
$-2(3a+2b-1)+3(a+4b-2)$
$a-2(2a+b)+3(3a-2)$
$-3(5a+b)+4(4a+b)$
$2a-4b-3(a-2b-2)$
$2(a+b)-3(2a+1)-2(b-3)$
$3(a-2b-2)+2(a+3b+1)$
$3a+2(2a+b-2)+5(b-2)$

Explanation:

Step1: Combine like terms

$3a - 2a + 4b + 3 - 7 = a + 4b - 4$

Step2: Distribute then combine terms

$3a + 8a - 2b = 11a - 2b$

Step3: Distribute then combine terms

$8a + 2b + 3a - 9b = 11a - 7b$

Step4: Distribute then combine terms

$8a - 8 + 4a - 4b = 12a - 4b - 8$

Step5: Distribute then combine terms

$7a - 14b + 14 + 7b = 7a - 7b + 14$

Step6: Distribute then combine terms

$3a + 6 - 4b - 12 + 2a + 2 = 5a - 4b - 4$

Step7: Distribute then combine terms

$2b - 8 - 3a - 6b - 9 = -3a - 4b - 17$

Step8: Distribute then combine terms

$-3a + 3b - 14a - 7b = -17a - 4b$

Step9: Distribute then combine terms

$4a - 2b - 4a - 12b = -14b$

Step10: Distribute then combine terms

$-6a - 4b + 2 + 3a + 12b - 6 = -3a + 8b - 4$

Step11: Distribute then combine terms

$a - 4a - 2b + 9a - 6 = 6a - 2b - 6$

Step12: Distribute then combine terms

$-15a - 3b + 16a + 4b = a + b$

Step13: Distribute then combine terms

$2a - 4b - 3a + 6b + 6 = -a + 2b + 6$

Step14: Distribute then combine terms

$2a + 2b - 6a - 3 - 2b + 6 = -4a + 3$

Step15: Distribute then combine terms

$3a - 6b - 6 + 2a + 6b + 2 = 5a - 4$

Step16: Distribute then combine terms

$3a + 4a + 2b - 4 + 5b - 10 = 7a + 7b - 14$

Answer:

1. $a + 4b - 4$
2. $11a - 2b$
3. $11a - 7b$
4. $12a - 4b - 8$
5. $7a - 7b + 14$
6. $5a - 4b - 4$
7. $-3a - 4b - 17$
8. $-17a - 4b$
9. $-14b$
10. $-3a + 8b - 4$
11. $6a - 2b - 6$
12. $a + b$
13. $-a + 2b + 6$
14. $-4a + 3$
15. $5a - 4$
16. $7a + 7b - 14$