Math questions? URGENT!!!?

Question

1. Which is a simplified form of the expression -4(3r – 2) – 2(r + 1)? 
2. Which is a simplified form of the expression -4(n + 1) – (n + 2)? 
3. Which is a simplified form of the expression -2b – 3(2b + 1)? 
4. Which is a simplified form of the expression 4(2z – 1) – 5z? 
5. Which is a simplified form of the expression -(z + 1) + 2(z – 2)? 
6. Which is a simplified form of the expression 2(y + 1) + 2(y – 2)? 
7. Which is a simplified form of the expression -3x – 1 – 5x + 4? 
8. Which is a simplified form of the expression 3a + 7 – a – 7?

Answer 1

1)

Given expression is

-4 ( 3r – 2 ) – 2 ( r + 1 )

Using distributive property: a(b + c) = ab + ac.

= (– 4)(3r) – (– 4)(2) – 2(r) – 2(1)

= – 12r + 8 – 2r – 2

Using commutative property of addition: a + b = b + a.

= – 12r  – 2r + 8 – 2

= – 14r + 6

Solution : - 4 ( 3r – 2 ) – 2 ( r + 1 ) = – 14r + 6.

Answer 2

2)

Given expression is

-4 (n + 1) – (n + 2)

Using distributive property: a×(b + c) = (a×b) + (a×c).

= (– 4)(n) + (– 4)(1) – n – 2

=  – 4n – 4 – n – 2

Using commutative property of addition: a + b = b + a.

=  – 4n  – n – 4 – 2

= – 5n  –  6

Solution : - 4 (n + 1) – (n + 2) = – 5n  –  6.

Answer 3

3)

Given expression is

– 2b – 3(2b + 1)

Using distributive property: a(b + c) = ab + ac.

= – 2b – 3(2b) – 3(1)

= – 2b – 6b – 3

= – 8b – 3

Solution : – 2b – 3(2b + 1) = – 8b – 3

Answer 4

4)

Given expression is

4(2z – 1) – 5z

Using distributive property: a(b + c) = ab + ac.

= 4(2z) – 4(1) – 5z

= 8z – 4 – 5z

Using commutative property of addition: a + b = b + a.

= 8z  – 5z – 4

= 3z – 4

Solution : 4(2z – 1) – 5z  = 3z – 4

Answer 5

5)

Given expression is

– (z + 1) + 2(z – 2)

Using distributive property: a(b + c) = ab + ac.

= – z – 1 + 2z – 2(2)

= – z – 1 + 2z – 4

Using commutative property of addition: a + b = b + a.

= – z + 2z – 1 – 4

Using commutative property of addition: a + b = b + a.

= 2z – z – 1 – 4

= z – 5

Solution : – (z + 1) + 2(z – 2) =  z – 5

Answer 6

6)

Given expression is

2(y + 1) + 2(y – 2)

Using distributive property: a(b + c) = ab + ac.

= 2(y) + 2(1) + 2(y) – 2(2)

= 2y + 2 + 2y – 4

Using commutative property of addition: a + b = b + a.

= 2y + 2y + 2 – 4

= 4y – 2

Solution :  2(y + 1) + 2(y – 2) = 4y – 2.

Answer 7

7)

Given expression is

 – 3x – 1 – 5x + 4

Using commutative property of addition: a + b = b + a.

= – 3x  – 5x – 1 + 4

Using commutative property of addition: a + b = b + a.

= – 3x  – 5x + 4 – 1

= – 8x + 3

Solution :  – 3x – 1 – 5x + 4 = – 8x + 3.

Answer 8

8)

Given expression is

3a + 7 – a – 7

Using commutative property of addition : a + b = b + a.

= 3a  – a + 7 – 7

= 2a + 7 – 7

Using the Additive Inverse property : a – a = 0

= 2a + 0

Using the Additive Identity property : a + 0 = a

= 2a

Solution :  3a + 7 – a – 7 = 2a.