1. If m = 2, find the value of:

(i) m – 2

Solution:

Given, m = 2

Now, substitute the value of m in the question

= 2 -2

= 0

(ii) 3m – 5

Solution:

Given, m = 2

Now, substitute the value of m in the question

= (3 × 2) – 5

= 6 – 5

= 1

(iii) 9 – 5m

Solution:

Given, m = 2

Now, substitute the value of m in the question

= 9 – (5 × 2)

= 9 – 10

= – 1

(iv) 3m² – 2m – 7

Solution:

Given, m = 2

Now, substitute the value of m in the question

= (3 × 2²) – (2 × 2) – 7

= (3 × 4) – (4) – 7

= 12 – 4 -7

= 12 – 11

= 1

(v) (5m/2) – 4

Solution:

Given, m = 2

Now, substitute the value of m in the question

= ((5 × 2)/2) – 4

= (10/2) – 4

= 5 – 4

= 1

2. If p = – 2, find the value of:

(i) 4p + 7

Solution:

Given, p = -2

Now, substitute the value of p in the question

= (4 × (-2)) + 7

= -8 + 7

= -1

(ii) – 3p² + 4p + 7

Solution:

Given, p = -2

Now, substitute the value of p in the question

= (-3 × (-2)²) + (4 × (-2)) + 7

= (-3 × 4) + (-8) + 7

= -12 – 8 + 7

= -20 + 7

= -13

(iii) – 2p³ – 3p² + 4p + 7

Solution:

Given, p = -2

Now, substitute the value of p in the question

= (-2 × (-2)³) – (3 × (-2)²) + (4 × (-2)) + 7

= (-2 × -8) – (3 × 4) + (-8) + 7

= 16 – 12 – 8 + 7

= 23 – 20

= 3

3. Find the value of the following expressions, when x = –1:

(i) 2x – 7

Solution:

Given, x = -1

Now, substitute the value of x in the question

= (2 × -1) – 7

= – 2 – 7

= – 9

(ii) – x + 2

Solution:

Given, x = -1

Now, substitute the value of x in the question

= – (-1) + 2

= 1 + 2

= 3

(iii) x² + 2x + 1

Solution:

Given that x = -1

Now, substitute the value of x in the question

= (-1)² + (2 × -1) + 1

= 1 – 2 + 1

= 2 – 2

= 0

(iv) 2x² – x – 2

Solution:

Given, x = -1

Now, substitute the value of x in the question

= (2 × (-1)²) – (-1) – 2

= (2 × 1) + 1 – 2

= 2 + 1 – 2

= 3 – 2

= 1

4. If a = 2, b = – 2, find the value of:

(i) a² + b²

Solution:

Given, a = 2, b = -2

Now, substitute the value of a and b in the question

= (2)² + (-2)²

= 4 + 4

= 8

(ii) a² + ab + b²

Solution:

Given, a = 2, b = -2

Now, substitute the value of a and b in the question

= 2² + (2 × -2) + (-2)²

= 4 + (-4) + (4)

= 4 – 4 + 4

= 4

(iii) a² – b²

Solution:

Given, a = 2, b = -2

Now, substitute the value of a and b in the question

= 2² – (-2)²

= 4 – (4)

= 4 – 4

= 0

5. When a = 0, b = – 1, find the value of the given expressions:

(i) 2a + 2b

Solution:

Given, a = 0, b = -1

Now, substitute the value of a and b in the question

= (2 × 0) + (2 × -1)

= 0 – 2

= -2

(ii) 2a² + b² + 1

Solution:

Given that a = 0, b = -1

Now, substitute the value of a and b in the question

= (2 × 0²) + (-1)² + 1

= 0 + 1 + 1

= 2

(iii) 2a²b + 2ab² + ab

Solution:

Given that a = 0, b = -1

Now, substitute the value of a and b in the question

= (2 × 0² × -1) + (2 × 0 × (-1)²) + (0 × -1)

= 0 + 0 +0

= 0

(iv) a² + ab + 2

Solution:

Given, a = 0, b = -1

Now, substitute the value of a and b in the question

= (0²) + (0 × (-1)) + 2

= 0 + 0 + 2

= 2

6. Simplify the expressions and find the value if x is equal to 2

(i) x + 7 + 4 (x – 5)

Solution:

Given, x = 2

We have,

= x + 7 + 4x – 20

= 5x + 7 – 20

Now, substitute the value of x in the equation

= (5 × 2) + 7 – 20

= 10 + 7 – 20

= 17 – 20

= – 3

(ii) 3 (x + 2) + 5x – 7

Solution:

Given, x = 2

We have,

= 3x + 6 + 5x – 7

= 8x – 1

Now, substitute the value of x in the equation

= (8 × 2) – 1

= 16 – 1

= 15

(iii) 6x + 5 (x – 2)

Solution:

Given, x = 2

We have,

= 6x + 5x – 10

= 11x – 10

Now, substitute the value of x in the equation

= (11 × 2) – 10

= 22 – 10

= 12

(iv) 4(2x – 1) + 3x + 11

Solution:

Given, x = 2

We have,

= 8x – 4 + 3x + 11

= 11x + 7

Now, substitute the value of x in the equation

= (11 × 2) + 7

= 22 + 7

= 29

7. Simplify these expressions and find their values if x = 3, a = – 1, b = – 2.

(i) 3x – 5 – x + 9

Solution:

Given, x = 3

We have,

= 3x – x – 5 + 9

= 2x + 4

Now, substitute the value of x in the equation

= (2 × 3) + 4

= 6 + 4

= 10

(ii) 2 – 8x + 4x + 4

Solution:

Given, x = 3

We have,

= 2 + 4 – 8x + 4x

= 6 – 4x

Now, substitute the value of x in the equation

= 6 – (4 × 3)

= 6 – 12

= – 6

(iii) 3a + 5 – 8a + 1

Solution:

Given, a = -1

We have,

= 3a – 8a + 5 + 1

= – 5a + 6

Now, substitute the value of a in the equation

= – (5 × (-1)) + 6

= – (-5) + 6

= 5 + 6

= 11

(iv) 10 – 3b – 4 – 5b

Solution:

Given, b = -2

We have,

= 10 – 4 – 3b – 5b

= 6 – 8b

Now, substitute the value of b in the equation

= 6 – (8 × (-2))

= 6 – (-16)

= 6 + 16

= 22

(v) 2a – 2b – 4 – 5 + a

Solution:

Given, a = -1, b = -2

We have,

= 2a + a – 2b – 4 – 5

= 3a – 2b – 9

Now, substitute the value of a and b in the equation

= (3 × (-1)) – (2 × (-2)) – 9

= -3 – (-4) – 9

= – 3 + 4 – 9

= -12 + 4

= -8

8. (i) If z = 10, find the value of z³ – 3(z – 10).

Solution:

Given, z = 10

We have,

= z³ – 3z + 30

Now, substitute the value of z in the equation

= (10)³ – (3 × 10) + 30

= 1000 – 30 + 30

= 1000

(ii) If p = – 10, find the value of p² – 2p – 100

Solution:

Given, p = -10

We have,

= p² – 2p – 100

Now, substitute the value of p in the equation

= (-10)² – (2 × (-10)) – 100

= 100 + 20 – 100

= 20

9. What should be the value of a if the value of 2x² + x – a equals to 5, when x = 0?

Solution:

Given, x = 0

We have,

2x² + x – a = 5

a = 2x² + x – 5

Now, substitute the value of x in the equation

a = (2 × 0²) + 0 – 5

a = 0 + 0 – 5

a = -5

10. Simplify the expression and find its value when a = 5 and b = – 3. 2(a² + ab) + 3 – ab

Solution:

Given, a = 5 and b = -3

We have,

= 2a² + 2ab + 3 – ab

= 2a² + ab + 3

Now, substitute the value of a and b in the equation

= (2 × 5²) + (5 × (-3)) + 3

= (2 × 25) + (-15) + 3

= 50 – 15 + 3

= 53 – 15

= 38