**Algebraic Expressions**

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

**(i) m – 2**

**Solution:-**

From the question it is given that m = 2

Then, substitute the value of m in the question

= 2 -2

= 0

**(ii) 3m – 5**

**Solution:-**

From the question it is given that m = 2

Then, substitute the value of m in the question

= (3 × 2) – 5

= 6 – 5

= 1

**(iii) 9 – 5m**

**Solution:-**

From the question it is given that m = 2

Then, substitute the value of m in the question

= 9 – (5 × 2)

= 9 – 10

= – 1

**(iv) 3m ^{2} – 2m – 7**

**Solution:-**

From the question it is given that m = 2

Then, substitute the value of m in the question

= (3 × 2^{2}) – (2 × 2) – 7

= (3 × 4) – (4) – 7

= 12 – 4 -7

= 12 – 11

= 1

**(v) (5m/2) – 4**

**Solution:-**

From the question it is given that m = 2

Then, 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:-**

From the question it is given that p = -2

Then, substitute the value of p in the question

= (4 × (-2)) + 7

= -8 + 7

= -1

**(ii) – 3p ^{2} + 4p + 7**

**Solution:-**

From the question it is given that p = -2

Then, 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) – 2p ^{3} – 3p^{2} + 4p + 7**

**Solution:-**

From the question it is given that p = -2

Then, 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:-**

From the question it is given that x = -1

Then, substitute the value of x in the question

= (2 × -1) – 7

= – 2 – 7

= – 9

**(ii) – x + 2**

**Solution:-**

From the question it is given that x = -1

Then, substitute the value of x in the question

= – (-1) + 2

= 1 + 2

= 3

**(iii) x ^{2} + 2x + 1**

**Solution:-**

From the question it is given that x = -1

Then, substitute the value of x in the question

= (-1)^{2} + (2 × -1) + 1

= 1 – 2 + 1

= 2 – 2

= 0

**(iv) 2x ^{2} – x – 2**

**Solution:-**

From the question it is given that x = -1

Then, 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) a ^{2} + b^{2}**

**Solution:-**

From the question it is given that a = 2, b = -2

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

= (2)^{2} + (-2)^{2}

= 4 + 4

= 8

**(ii) a ^{2} + ab + b^{2}**

**Solution:-**

From the question it is given that a = 2, b = -2

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

= 2^{2} + (2 × -2) + (-2)^{2}

= 4 + (-4) + (4)

= 4 – 4 + 4

= 4

**(iii) a ^{2} – b^{2}**

**Solution:-**

From the question it is given that a = 2, b = -2

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

= 2^{2} – (-2)^{2}

= 4 – (4)

= 4 – 4

= 0

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

**(i) 2a + 2b**

**Solution:-**

From the question it is given that a = 0, b = -1

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

= (2 × 0) + (2 × -1)

= 0 – 2

= -2

**(ii) 2a ^{2} + b^{2} + 1**

**Solution:-**

From the question it is given that a = 0, b = -1

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

= (2 × 0^{2}) + (-1)^{2} + 1

= 0 + 1 + 1

= 2

**(iii) 2a ^{2}b + 2ab^{2} + ab**

**Solution:-**

From the question it is given that a = 0, b = -1

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

= (2 × 0^{2} × -1) + (2 × 0 × (-1)^{2}) + (0 × -1)

= 0 + 0 +0

= 0

**(iv) a ^{2} + ab + 2**

**Solution:-**

From the question it is given that a = 0, b = -1

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

= (0^{2}) + (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:-**

From the question it is given that x = 2

We have,

= x + 7 + 4x – 20

= 5x + 7 – 20

Then, 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:-**

From the question it is given that x = 2

We have,

= 3x + 6 + 5x – 7

= 8x – 1

Then, substitute the value of x in the equation

= (8 × 2) – 1

= 16 – 1

= 15

**(iii) 6x + 5 (x – 2)**

**Solution:-**

From the question it is given that x = 2

We have,

= 6x + 5x – 10

= 11x – 10

Then, substitute the value of x in the equation

= (11 × 2) – 10

= 22 – 10

= 12

**(iv) 4(2x – 1) + 3x + 11**

**Solution:-**

From the question it is given that x = 2

We have,

= 8x – 4 + 3x + 11

= 11x + 7

Then, 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:-**

From the question it is given that x = 3

We have,

= 3x – x – 5 + 9

= 2x + 4

Then, substitute the value of x in the equation

= (2 × 3) + 4

= 6 + 4

= 10

**(ii) 2 – 8x + 4x + 4**

**Solution:-**

From the question it is given that x = 3

We have,

= 2 + 4 – 8x + 4x

= 6 – 4x

Then, substitute the value of x in the equation

= 6 – (4 × 3)

= 6 – 12

= – 6

**(iii) 3a + 5 – 8a + 1**

**Solution:-**

From the question it is given that a = -1

We have,

= 3a – 8a + 5 + 1

= – 5a + 6

Then, substitute the value of a in the equation

= – (5 × (-1)) + 6

= – (-5) + 6

= 5 + 6

= 11

**(iv) 10 – 3b – 4 – 5b**

**Solution:-**

From the question it is given that b = -2

We have,

= 10 – 4 – 3b – 5b

= 6 – 8b

Then, substitute the value of b in the equation

= 6 – (8 × (-2))

= 6 – (-16)

= 6 + 16

= 22

**(v) 2a – 2b – 4 – 5 + a**

**Solution:-**

From the question it is given that a = -1, b = -2

We have,

= 2a + a – 2b – 4 – 5

= 3a – 2b – 9

Then, 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 z ^{3} – 3(z – 10).**

**Solution:-**

From the question it is given that z = 10

We have,

= z^{3} – 3z + 30

Then, 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 p ^{2} – 2p – 100**

**Solution:-**

From the question it is given that p = -10

We have,

= p^{2} – 2p – 100

Then, 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 2x ^{2} + x – a equals to 5, when x = 0?**

**Solution:-**

From the question it is given that x = 0

We have,

2x^{2} + x – a = 5

a = 2x^{2} + x – 5

Then, substitute the value of x in the equation

a = (2 × 0^{2}) + 0 – 5

a = 0 + 0 – 5

a = -5

**10. Simplify the expression and find its value when a = 5 and b = – 3.**

**2(a ^{2} + ab) + 3 – ab**

**Solution:-**

From the question it is given that a = 5 and b = -3

We have,

= 2a^{2} + 2ab + 3 – ab

= 2a^{2} + ab + 3

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

= (2 × 5^{2}) + (5 × (-3)) + 3

= (2 × 25) + (-15) + 3

= 50 – 15 + 3

= 53 – 15

= 38