Chapter 9 Algebraic Expressions and Identities mcqs & important questions mathematics |class 8th

MCQ Questions for Class 8 Maths: Ch 9 Algebraic Expressions and Identities

1. Expressions consists of _____________ and _______________.

(a) variables, constants

(b) identities

(c) expressions

(d) none of these

► (a) variables, constants

2. Which of the following is an expression?

(a) 1/2

(b) 3

(c) 3x-2

(d) 2

► (c) 3x-2

3. The coefficient of x in the expression -7x +5 is

(a) 5        

(b) -7

(c) 7

(d) 0

► (b) -7

4. The number of terms in the expression 2x²+3x+5 is

(a) 1      

(b) 2

(c) 3

(d) 5
► (c) 3

5. Like terms in the expression 7x,5x²,7y, -5yx, -9x², are
(a) 7x, -5yx     
(b) 5x², -5yx
(c) 5x², -9x²
(d) 7x, 7y
► (c) 5x², -9x²

6. Terms are added to form ___________.
(a) expressions
(b) terms
(c) identities
(d) none of these
► (a) expressions

7. Add: 7xy + 5yz – 3zx, 4yz + 9zx – 4y, –3xz + 5x – 2xy.
(a) 5xy + 3zx + 5x – 4y
(b) 5xy + 9yz +2zx + 5x – 4y
(c) 5xy + 9yz +3zx + 5x – 4y
(d) 5xy + 9yz +3zx + 4y
► (c) 5xy + 9yz +3zx + 5x – 4y

8. The expression x + y + z is in
(a) one variable
(b) no variable
(c) three variables
(d) two variables
► (c) three variables

9. Which of the following is a monomial ?
(a) 4x²
(b) a + 6
(c) a + 6 + c
(d) a + b + c + d

► (a) 4x²

10. How many terms are there in the expression 5 – 3xy ?

(a) 1

(b) 2

(c) 3

(d) 5

► (b) 2

11. How many terms are there in the expression 5xy + 9yz + 3zx + 5x – 4y ?

(a) 1

(b) 3

(c) 4

(d) 5

► (d) 5

12. If x = 3 is solution of x² + kx + 15, value of k is

(a) k = -8, x = 3

(b) k = 8, x = 5

(c) k = 6, x = 5

(d) None of above

► (a) k = -8, x = 3

13. The coefficient in the term -5x is

(a) 5

(b) -5

(c) 1

(d) 2

► (b) -5

14. n (4 + m) = 4n + ___ 

(a) 4m

(b) 4n

(c) 4mn

(d) nm

► (d) nm

15. The like terms of the following are

(a) x, 3x

(b) x, 2y

(c) 2y, 6xy

(d) 3x, 2y

► (a) x, 3x

16. Value of expression ‘a(a²+a +1)+5’ for ‘ a’ = 0 is

(a) a+5      

(b) 1

(c) 6

(d) 5
► (d) 5

17. Which of the following is like term as 7xy?
(a) 9
(b) 9x
(c) 9y
(d) 9xy
► (d) 9xy

18. The area of triangle is’ xy’ where’ x’ is length and ‘y’ is breadth. If the length of rectangle is increased by 5 units and breadth is decreased by 3 units, the new area of rectangle will be
(a) (x-y)(x+3) 
(b) (xy+15)
(c) (x+5)(y-3)
(d) (xy+5-3)
► (c) (x+5)(y-3)

19. The expression 7xy has the factors
(a) 7,x,y         
(b) x,y
(c) 7,x
(d) 7,y
► (a) 7,x,y         

20. Which of the following is a binomial?
(a) 4x + y + 2
(b) 2x + 7
(c) 3x + 4y – 6
(d) 3x
► (b) 2x + 7

21. When numbers/literals are added or subtracted, they are called _________.
(a) identities
(b) expressions
(c) variables
(d) terms
► (d) terms

22. The volume of rectangular box whose length, breadth and height is 2p,4q.8r respectively is
(a) 14pqr   
(b) 2p+4q+8r
(c) 64pqr
(d) 64
► (c) 64pqr

Algebraic Expressions and Identities Class 8 Extra important Questions Short Answer Type

Question 11.
Simplify the following:
(i) a² (b² – c²) + b² (c² – a²) + c² (a² – b²)
(ii) x²(x – 3y²) – xy(y² – 2xy) – x(y³ – 5x²)
Solution:
(i) a² (b² – c²) + b² (c² – a²) + c² (a² – b²)
= a²b² – a²c²) + b²c² – b²a²) + c²a² – c²b²)
= 0
(ii) x²(x – 3y²) – xy(y² – 2xy) – x(y³ – 5x²)
= x³ – 3x²y² – xy³ + 2x²y² – xy³ + 5x³
= x³ + 5x³ – 3x²y² + 2x²y² – xy³ – xy³
= 6x³ – x²y² – 2xy³

Question 12.
Multiply (3x² + 5y²) by (5x² – 3y²)
Solution:
(3x² + 5y²) × (5x² – 3y²)
= 3x²(5x² – 3y²) + 5y²(5x² – 3y²)
= 15x⁴ – 9x²y² + 25x²y² – 15y⁴
= 15x⁴ + 16x²y² – 15y⁴

Question 13.
Multiply (6x² – 5x + 3) by (3x² + 7x – 3)
Solution:
(6x² – 5x + 3) × (3x² + 7x – 3)
= 6x²(3x² + 7x – 3) – 5x(3x² + 7x – 3) + 3(3x² + 7x – 3)
= 18x⁴ + 42x³ – 18x² – 15x³ – 35x² + 15x + 9x² + 21x – 9
= 18x⁴ + 42x³ – 15x³ – 18x² – 35x² + 9x² + 15x + 21x – 9
= 18x⁴ + 27x³ – 44x² + 36x – 9

Question 14.
Simplify:
2x²(x + 2) – 3x (x² – 3) – 5x(x + 5)
Solution:
2x²(x + 2) – 3x(x² – 3) – 5x(x + 5)
= 2x³ + 4x² – 3x³ + 9x – 5x² – 25x
= 2x³ – 3x³ – 5x² + 4x² + 9x – 25x
= -x³ – x² – 16x

Question 15.
Multiply x² + 2y by x³ – 2xy + y³ and find the value of the product for x = 1 and y = -1.
Solution:
(x² + 2y) × (x³ – 2xy + y³)
= x²(x³ – 2xy + y³) + 2y(x³ – 2xy + y³)
= x⁵ – 2x³y + x²y³ + 2x³y – 4xy² + 2y⁴
= x⁵ + x²y³ – 4xy² + 2y⁴
Put x = 1 and y = -1
= (1)⁵ + (1)² (-1)³ – 4(1)(-1)² + 2(-1)⁴
= 1 + (1) (-1) – 4(1)(1) + 2(1)
= 1 – 1 – 4 + 2
= -2

Question 16.
Using suitable identity find:
(i) 48² (NCERT Exemplar)
(ii) 96²
(iii) 231² – 131²
(iv) 97 × 103
(v) 181² – 19² = 162 × 200 (NCERT Exemplar)
Solution:

Question 17.

Solution:

Question 18.
Verify that (11pq + 4q)² – (11pq – 4q)² = 176pq² (NCERT Exemplar)
Solution:
LHS = (11pq + 4q)² – (11pq – 4q)² = (11pq + 4q + 11pq – 4q) × (11pq + 4q – 11pq + 4q)
[using a² -b² = (a – b) (a + b), here a = 11pq + 4q and b = 11 pq – 4q]
= (22pq) (8q)
= 176 pq²
= RHS.
Hence Verified.

Question 19.
Find the value of \(\frac { { 38 }^{ 2 }-{ 22 }^{ 2 } }{ 16 }\), using a suitable identity. (NCERT Exemplar)
Solution:

Question 20.
Find the value of x, if 10000x = (9982)² – (18)² (NCERT Exemplar)
Solution:
RHS = (9982)² – (18)² = (9982 + 18)(9982 – 18)
[Since a² -b² = (a + b) (a – b)]
= (10000) × (9964)
LHS = (10000) × x
Comparing L.H.S. and RHS, we get
10000x = 10000 × 9964
x = 9964