Question

directions: simplify each expression by combining like terms. 1. 8y - 9y 2. 3x - 7x + 1 3. 8a - 6 + a - 1 4. -2y + 14 - 9y + 5 5. -x - 2 + 15x 6. -7w - 5 - 7w + 9 7. 8d - 4 - d - 2 8. 40 - 9x + 4x + 5 9. 9a + 8 - 2a - 3 - 5a 10. 4xy - 6xy + 5y - 9x 11. 7x + 2y + 5 - 5x + 9y - 1 12. -5f - 7g + f - 5g - 4 + f 13. -6 + 3a - b - 4a + 4b + 5 14. 6n² - 2n - 3 + 5n² - 9n - 6 15. 8c² - c + 3 + 2c² - c + 2 16. -12x²y - 3x²y 17. 6a²b² + 3ab² - a²b² - 4ab² 18. 19x²y - 4xy² + 5xy² - 16x²y 19. write the perimeter of the rectangle as a simplified expression. 20. write the perimeter of the triangle as a simplified expression.

Explanation:

Step1: Combine like - terms for 8y - 9y

$(8 - 9)y=-y$

Step2: Combine like - terms for 3x - 7x + 1

$(3 - 7)x+1=-4x + 1$

Step3: Combine like - terms for 8a - 6 + a - 1

$(8a + a)+(-6 - 1)=9a-7$

Step4: Combine like - terms for - 2y + 14 - 9y + 5

$(-2y-9y)+(14 + 5)=-11y + 19$

Step5: Combine like - terms for - x - 2+15x

$(-x + 15x)-2 = 14x-2$

Step6: Combine like - terms for - 7w - 5 - 7w + 9

$(-7w-7w)+(-5 + 9)=-14w + 4$

Step7: Combine like - terms for 8d - 4 - d - 2

$(8d - d)+(-4 - 2)=7d-6$

Step8: Combine like - terms for 40 - 9x + 4x + 5

$(-9x + 4x)+(40 + 5)=-5x + 45$

Step9: Combine like - terms for 9a + 8 - 2a - 3 - 5a

$(9a-2a-5a)+(8 - 3)=2a + 5$

Step10: Combine like - terms for 4xy - 6xy+5y - 9x

$(4xy-6xy)+5y - 9x=-2xy + 5y - 9x$

Step11: Combine like - terms for 7x + 2y + 5 - 5x + 9y - 1

$(7x-5x)+(2y + 9y)+(5 - 1)=2x + 11y+4$

Step12: Combine like - terms for - 5f-7g + f-5g - 4 + f

$(-5f + f + f)+(-7g-5g)-4=-3f-12g-4$

Step13: Combine like - terms for - 6 + 3a - b - 4a + 4b + 5

$(3a-4a)+(-b + 4b)+(-6 + 5)=-a + 3b-1$

Step14: Combine like - terms for 6n² - 2n - 3 + 5n² - 9n - 6

$(6n²+5n²)+(-2n-9n)+(-3 - 6)=11n²-11n - 9$

Step15: Combine like - terms for 8c² - c + 3 + 2c² - c + 2

$(8c²+2c²)+(-c - c)+(3 + 2)=10c²-2c + 5$

Step16: Combine like - terms for - 12x²y-3x²y

$(-12 - 3)x²y=-15x²y$

Step17: Combine like - terms for 6a²b² + 3ab² - a²b² - 4ab²

$(6a²b²-a²b²)+(3ab²-4ab²)=5a²b² - ab²$

Step18: Combine like - terms for 19x²y - 4xy² + 5xy² - 16x²y

$(19x²y-16x²y)+(-4xy² + 5xy²)=3x²y+xy²$

Step19: Perimeter of rectangle

$2(7x + 1)+2(x - 3)=14x+2 + 2x-6=(14x + 2x)+(2 - 6)=16x-4$

Step20: Perimeter of triangle

$(3y + 5)+6y+(y - 4)=(3y+6y + y)+(5 - 4)=10y + 1$

Answer:

1. $-y$
2. $-4x + 1$
3. $9a-7$
4. $-11y + 19$
5. $14x-2$
6. $-14w + 4$
7. $7d-6$
8. $-5x + 45$
9. $2a + 5$
10. $-2xy + 5y - 9x$
11. $2x + 11y+4$
12. $-3f-12g-4$
13. $-a + 3b-1$
14. $11n²-11n - 9$
15. $10c²-2c + 5$
16. $-15x²y$
17. $5a²b² - ab²$
18. $3x²y+xy²$
19. $16x-4$
20. $10y + 1$