When solving algebraic expressions, the value depends on the variables in the expression. We often need to find these values, like when checking if a certain variable value satisfies an equation.
For instance, in geometry or everyday math, finding the value of an expression is common. Take the area of a square, calculated as l² where l is the length of a side. If l is 5 cm, the area is 5² cm², or 25 cm². If the side is 10 cm, the area is 10² cm², or 100 cm².
Lets have a look at the few examples which will help you in solving the questions ahead –
Example 1: If m = 2, find the value of 3m – 5.
Step 1: Substitute m = 2 into the expression: 3(2) – 5.
Step 2: Calculate: 6 – 5 = 1.
Example 2: If p = -2, find the value of 4p + 7.
Step 1: Substitute p = -2 into the expression: 4(-2) + 7.
Step 2: Calculate: -8 + 7 = -1.
Example 3: Find the value of 2x – 7 when x = -1.
Step 1: Substitute x = -1 into the expression: 2(-1) – 7.
Step 2: Calculate: -2 – 7 = -9.
Example 4: If a = 2, b = -2, find the value of a² + ab + b².
Step 1: Substitute a = 2 and b = -2: (2)² + 2(-2) + (-2)².
Step 2: Calculate: 4 – 4 + 4 = 4.
The approach is key in solving the exercises in exercise 10.2 chapter 10 algebraic expressions.
Question and Answers for Class 7 Maths Exercise 10.2 Chapter 10 Algebraic Expressions
1. If m = 2, find the value of –
(i) m – 2:
2 – 2 = 0
(ii) 3m – 5:
3 * 2 – 5
= 6 – 5
= 1
(iii) 9 – 5m:
9 – 5 * 2
= 9 – 10
= -1
(iv) 3m² – 2m – 7:
3 * 2² – 2 * 2 – 7
= 3 * 4 – 4 – 7
= 12 – 4 – 7
= 1
(v) 5m/2 – 4:
(5 * 2)/2 – 4
= 10/2 – 4
= 5 – 4
= 1
2. If p = –2, find the value of –
(i) 4p + 7:
4 * (-2) + 7
= -8 + 7
= -1
(ii) –3p² + 4p + 7:
-3 * (-2)² + 4 * (-2) + 7
= -3 * 4 – 8 + 7
= -12 – 8 + 7
= -13
(iii) –2p³ – 3p² + 4p + 7:
-2 * (-2)³ – 3 * (-2)² + 4 * (-2) + 7
= -2 * -8 – 3 * 4 – 8 + 7
= 16 – 12 – 8 + 7
= 3
3. Find the value of the following expressions, when x = –1 –
(i) 2x – 7:
2 * (-1) – 7
= -2 – 7
= -9
(ii) –x + 2:
-(-1) + 2
= 1 + 2
= 3
(iii) x² + 2x + 1:
(-1)² + 2 * (-1) + 1
= 1 – 2 + 1
= 0
(iv) 2x² – x – 2:
2 * (-1)² – (-1) – 2
= 2 * 1 + 1 – 2
= 2 + 1 – 2
= 1
4. If a = 2, b = –2, find the value of –
(i) a² + b²:
a² = 2² = 4
b² = (–2)² = 4
a² + b² = 4 + 4 = 8
(ii) a² + ab + b²:
a² = 2² = 4
ab = 2 * (–2) = –4
b² = (–2)² = 4
a² + ab + b² = 4 – 4 + 4 = 4
(iii) a² – b²:
a² = 2² = 4
b² = (–2)² = 4
a² – b² = 4 – 4 = 0
5. When a = 0, b = –1, find the value of the given expressions –
(i) 2a + 2b
2a = 2 * 0 = 0
2b = 2 * (–1) = –2
2a + 2b = 0 – 2 = –2
(ii) 2a² + b² + 1
2a² = 2 * 0² = 0
b² = (–1)² = 1
2a² + b² + 1 = 0 + 1 + 1 = 2
(iii) 2a²b + 2ab² + ab
2a²b = 2 * 0² * (–1) = 0
2ab² = 2 * 0 * (–1)² = 0
ab = 0 * (–1) = 0
2a²b + 2ab² + ab = 0 + 0 + 0 = 0
(iv) a² + ab + 2
a² = 0² = 0
ab = 0 * (–1) = 0
a² + ab + 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)
Simplifying x + 7 + 4 (x – 5)
= 7 + x + 4x -20
= 5x – 13
Putting the value of x = 2 in above equation
5(2) – 13
= 10 – 13
= -3 Ans
Method 2
Substitute x with 2 in the original equation
2 + 7 + 4 (2 – 5)
Now simplify inside the brackets:
2 + 7 + 4 * (–3)
Multiply 4 with –3:
2 + 7 – 12
= 9 – 2
= -3 Ans
(ii) 3 (x + 2) + 5x – 7:
Simplifying 3 (x + 2) + 5x – 7
= 3x + 6 + 5x – 7
= 8x -1
Putting the value of x = 2 in the above equation
8(2) – 1
= 16 – 1
= 15
Method 2
Substitute the value of x with 2 in the original equation
3 (2 + 2) + 5 * 2 – 7
Now simplify inside the brackets:
3 * 4 + 10 – 7
Multiply 3 with 4:
12 + 10 – 7
Now add and subtract in order:
15
(iii) 6x + 5 (x – 2):
Simplifying 6x + 5 (x – 2)
= 6x + 5x – 10
= 11x – 10
Putting the value of x = 2 in the above equation
11(2) – 10
= 12 Ans
Method 2
Substitute the value of x with 2 in the original equation
6 * 2 + 5 (2 – 2)
Now simplify inside the brackets:
12 + 5 * 0
Multiply 5 with 0:
12 + 0
Now add and subtract in order:
12 Ans
(iv) 4 (2x – 1) + 3x + 11:
Simplifying 4 (2x – 1) + 3x + 11
= 8x – 4 + 3x + 11
= 11x + 7
Putting the value of x = 2 in the above equation
11(2) + 7
= 29 Ans
Method 2
Substitute the value of x with 2 in the original equation
4 (2 * 2 – 1) + 3 * 2 + 11
Now simplify inside the brackets:
4 (4 – 1) + 6 + 11
Multiply 4 with 3:
4 * 3 + 6 + 11
Now add and subtract in order:
12 + 6 + 11
= 29 Ans
7. Simplify these expressions and find their values if x = 3, a = –1, b = –2:
(i) 3x – 5 – x + 9:
Simplifying 3x – 5 – x + 9
= 2x + 4
Putting the value of x = 3 in above equation
2(3) + 4
= 6 + 4
= 10 Ans
(ii) 2 – 8x + 4x + 4:
Simplifying 2 – 8x + 4x + 4
= -4x + 6
Putting the value of x = 3 in above equation
-4(3) + 6
= -12 + 6
= -6 Ans
(iii) 3a + 5 – 8a + 1:
Simplifying 3a + 5 – 8a + 1
= -5a + 6
Putting the value of a = –1 in above equation
-5(-1) + 6
= 5 + 6
= 11 Ans
(iv) 10 – 3b – 4 – 5b:
Simplifying 10 – 3b – 4 – 5b
= -8b + 6
Putting the value of b = –2 in above equation
-8(-2) + 6
= 16 + 6
= 22 Ans
(v) 2a – 2b – 4 – 5 + a
Simplifying 2a – 2b – 4 – 5 + a
= 2a + a – 2b – 4 – 5
= 3a – 2b – 9
Putting the values of a = –1 and b = –2 in the above equation
= 3(-1) – 2(-2) – 9
= -3 + 4 – 9
= -8 Ans
8. (i) If z = 10, find the value of z³ – 3(z – 10)
Simplifying z³ – 3(z – 10)
= z³ – 3z + 30
Putting the value of z = 10 in above equation
= 10³ – 3(10) + 30
= 1000 – 30 + 30
= 1000 Ans
(ii) If p = –10, find the value of p² – 2p – 100.
Simplifying p² – 2p – 100
= p² – 2p – 100
Putting the value of p = –10 in above equation
= (-10)² – 2(-10) – 100
= 100 + 20 – 100
= 20 Ans
9. What should be the value of a if the value of 2x² + x – a equals 5, when x = 0?
Simplifying 2x² + x – a = 5
= 2x² + x – a
Putting the value of x = 0 in above equation
= 2(0)² + 0 – a = 5
= -a = 5
Thus, a = -5 Ans
10. Simplify the expression and find its value when a = 5 and b = –3
Simplifying the expression 2(a² + ab) + 3 – ab
= 2a² + 2ab + 3 – ab
= 2a² + ab + 3
Putting the values of a = 5 and b = –3 in above equation
= 2(5)² + 5(-3) + 3
= 2(25) – 15 + 3
= 50 – 15 + 3
= 38 Ans
Additional Multiple-Choice Questions(MCQ), Based on Ex. 10.2 NCERT Book under CBSE Curriculum
Question 1. If m = 2, what is the value of 3m² – 2m – 7?
a) 5
b) -1
c) 1
d) 3
Answer:
b) -1
Question 2. If p = –2, find the value of –3p² + 4p + 7.
a) 15
b) 17
c) 19
d) 21
Answer:
c) 19
Question 3. For x = –1, what is the value of x² + 2x + 1?
a) 0
b) 2
c) 4
d) -2
Answer:
a) 0
Question 4. If a = 2 and b = –2, what is the value of a² – b²?
a) 0
b) 4
c) 8
d) 16
Answer:
c) 8
Question 5. When a = 0 and b = –1, find the value of 2a² + b² + 1.
a) 0
b) 1
c) 2
d) -1
Answer:
c) 2
Question 6. Simplify and find the value of 3 (x + 2) + 5x – 7 when x = 2.
a) 16
b) 18
c) 20
d) 22
Answer:
a) 16
Question 7. For x = 3, a = –1, b = –2, what is the value of 3a + 5 – 8a + 1?
a) -1
b) 0
c) 3
d) 7
Answer:
b) 0
Question 8. If z = 10, find the value of z³ – 3(z – 10).
a) 970
b) 1000
c) 1030
d) 1060
Answer:
a) 970
Question 9. What should be the value of a if the value of 2x² + x – a is 5 when x = 0?
a) -5
b) 0
c) 5
d) 10
Answer:
c) 5
Question 10. Find the value of 4 (2x – 1) + 3x + 11 when x is equal to 2.
a) 23
b) 25
c) 27
d) 29
Answer:
b) 25
11. If x = 3 and y = -2, what is the value of the expression 2x² – 3xy + y²?
a) 25
b) 19
c) 13
d) 7
Answer:
b) 19
12. Simplify the expression 4a – 2(a – b) + 3b and find its value when a = 5 and b = -3.
a) 16
b) 14
c) 12
d) 10
Answer:
a) 16
13. If p = -1 and q = 2, evaluate the expression p³ + 3pq + q³.
a) 5
b) 3
c) 1
d) -1
Answer:
c) 1
14. The expression 5m – 2n is equal to 1 when m = 2. What is the value of n?
a) 4
b) 3
c) 2
d) 1
Answer:
b) 3
15. Simplify the expression 3(x + y) – 2(x – y) and find its value when x = 4 and y = -2.
a) 4
b) 6
c) 8
d) 10
Answer:
c) 8
16. If a = 1 and b = -1, what is the value of the expression a² + b² – 2ab?
a) 0
b) 1
c) 2
d) 4
Answer:
c) 2
17. Evaluate the expression 2x³ – 3x² + x – 5 when x = -1.
a) -11
b) -9
c) -7
d) -5
Answer:
a) -11
18. If x = 2 and y = 3, what is the value of the expression x²y – xy²?
a) -6
b) 0
c) 6
d) 12
Answer:
c) 6
19. Simplify the expression 4m – 2(n – m) + 3n and find its value when m = 3 and n = -2.
a) 16
b) 14
c) 12
d) 10
Answer:
b) 14
20. If p = 0 and q = 5, evaluate the expression p² – 2pq + q².
a) 0
b) 5
c) 10
d) 25
Answer:
d) 25
Worksheet for Practice – Exercise 10.2 Chapter 10 Algebraic Expressions
- If x = 4, find the value of 6x – x² + 3.
- Simplify 2y + 3y – 5 when y = –1.
- Evaluate a² + 2ab – b² for a = –3 and b = 2.
- Find the value of m³ + 4m when m = –2.
- If n = –4, calculate the value of –n³ + 2n² – 5n.
- Simplify the expression 3p² – 2p + 1 for p = –1.
- For a = 3 and b = –3, evaluate the expression a² – b² + 2ab.
- If x = –5, find the value of –3x² + 10x – 6.
- Simplify 4c – 3d + 2 when c = 2 and d = –3.
- Evaluate the expression 5k² – 2k + 3 for k = –2.
- If z = 1/2, find the value of 8z² – 2z + 5/4.
- For t = –1/3, calculate the value of –9t² – t + 1.
- Simplify 7u² – 2uv + v² for u = 1 and v = –1.
- If p = 1/4 and q = 1/2, find the value of 4p² + 3pq + 2q².
- Evaluate the expression 2x² – 3xy + y² for x = –3 and y = 2.
Answers:
- 19
- -10
- -17
- -16
- 60
- 6
- 0
- 89
- 19
- 27
- 4
- 4/3
- 6
- 1.25
- 25
