Evaluate each expression for a = 9, b = -3, c = -2, d = 7. Showyour work.1. A -cd2. 2b3+ c2a+d−cb4. (a–b)2+ d(a + c)5. 4c –(b –a)ab-5a7. 2bc+ d(12 –5)8. B+ 0.5[8 –(2c + a)]Simplify each expression using the Distributive Property.9.5(2g –8)10.7(y + 3)11. -3(4w–3)12. (6r + 3)2Simplify each expression, showing all work.13.8(x + 1) –12x14.6w –7 + 12w –3z15.9n –8 + 3(2n –11)16.3(7x + 4y) –2(2x + y)17. (15+ 8d)(-5) –24d + d18. 9(b –1) –c + 3b + c19. 20f–4(5f + 4) + 1620.8(h –4) –h–(h + 7)3.6.

1) 23; -8; 19; 73; 4; -76; 61; -6

10g - 40; 7y + 21; -12w + 9; 6r+3

2) -4x +8; 18w -3z -7; 15n - 41; 17x+10y; -75 - 63d; 12b-9; 0; 6h -39

Explanation:

a = 9, b = -3, c = -2, d = 7

1. a -cd = 9 - (-2)(7)

= 9 + 14 = 23

2. 2b+ c = 2(-3) + (-2)

= -6 -2 = -8

3. 2a+d−cb = 2(9) + 7 -(-2)(-3)

= 18 +7 -(6) = 25-6 = 19

4. (a–b)2+ d(a + c) = (9-(-3))*2 + 7(9+(-2))

= (9+3)*2 + 7(9-2) = 12*2 + 7(7)

= 24 + 49 = 73

5. 4c –(b –a) = 4(-2) - (-3 -9)

= -8 - (-12) = -8+12 = 4

6. ab-5a = 9(-3) - 5(9)

= -27 -49 = -76

7. 2bc+ d(12 –5) = 2(-3)(-2) + 7(12-5)

= 2(6) + 7(7) = 12 + 49 = 61

8. b + 0.5[8 –(2c + 2a)]

= -3 + 0.5[8-(2*-2 + 2*9)]

= -3 + 0.5(8-(-4+18)) = -3+0.5(8-14)

= -3+0.5(-6) = -3-3 = -6

Using Distributive Property

9. 5(2g –8) = 5*2g - 5*8

= 10g - 40

10. 7(y + 3) = 7*y + 7*3

= 7y + 21

11. -3(4w–3) = -3*4w -3(-3)

= -12w + 9

12. (6r + 3) = 1(6r + 3)

= 1*6r + 1*3

= 6r + 3

2) Simplify each expression

13. 8(x + 1) –12x = 8x + 8 -12x

= 8x -12x + 8 = -4x +8

14. 6w –7 + 12w –3z

= 6w+12w –3z –7

= 18w -3z -7

15. 9n –8 + 3(2n –11)

= 9n -8 +6n -33 = 15n - 41

16. 3(7x + 4y) –2(2x + y)

= 21x +12y -4x-2y = 21x -4x +12y-2y

= 17x + 10y

17. (15+ 8d)(-5) –24d + d

= -5(15) -5(8d) -24d + d

= -75 -40d -24d +d

= -75 - 63d

18. 9(b –1) –c + 3b + c

= 9b -9 -c +3b +c = 9b +3b -c +c -9

= 12b -9

19. 20f–4(5f + 4) + 16

= 20f -20f -16 +16 = 0

20. 8(h –4) –h–(h + 7)

= 8h - 32 -h -h -7

= 8h -2h -32-7

= 6h -39

pattern wax

explanation:

pattern wax is used for casting restoration as part of lost-wax technique.