RBSE Class 8 Maths Important Questions Chapter 9 Algebraic Expressions and Identities

Rajasthan Board RBSE Class 8 Maths Important Questions Chapter 9 Algebraic Expressions and Identities Important Questions and Answers.

RBSE Class 8 Maths Chapter 9 Important Questions Algebraic Expressions and Identities

Multiple Choice Questions:

Question 1.
The coefficient of x⁵ in \(\frac{8}{5}\)x⁵ is
(a) \(\frac{8}{5}\)
(b) 5
(c) 8
(d) \(\frac{5}{8}\)
Answer:
(a) \(\frac{8}{5}\)

Question 2.
The coefficient of yz in \(\frac{15}{16}\)xyz is
(a) \(\frac{15}{16}\)z
(b) \(\frac{15}{16}\)x
(c) \(\frac{15}{16}\)y
(d) \(\frac{15}{16}\)
Answer:
(b) \(\frac{15}{16}\)x

Question 3.
The total number of terms in the expression 8x² + 2xy + 3x² + 2y² + 2x² is
(a) 3
(b) 2
(c) 5
(d) 4
Answer:
(a) 3

Question 4.
The sum of the terms 4xy, 3.5xy, - 2xy, 2xz is
(a) 2.5xy + 5.2xz
(b) 5.5xy + 2xz
(c) 2.5xy + 5xz
(d) 5.5xy + 2xy
Answer:
(b) 5.5xy + 2xz

Question 5.
The product of 3x (x + y) is
(a) 3x² + 3xy
(b) 3x² + y
(c) x² + 3xy
(d) 3x + 3y
Answer:
(a) 3x² + 3xy

Question 6.
Subtraction 5a + 2b from 2a + 3b is
(a) 3a + 2b
(b) 2a + 3b
(c) -3a + b
(d) 5a - 3b
Answer:
(c) -3a + b

Question 7.
If x = 2 and y = 3, then the value of 3x + 3y is
(a) 15
(b) 8
(c) 9
(d) 18
Answer:
(a) 15

Question 8.
The product of xy, yz and zx is
(a) 2xyz
(b) x²y²z²
(c) xy + yz + zx
(d) x³y³z³
Answer:
(b) x²y²z²

Fill in the blanks

Question 1.
The coefficient of x⁴ in \(\frac{2}{8}\)x⁴ is ............... .
Answer:
\(\frac{2}{8}\)

Question 2.
The solution of 8xyz - 5xyz is ................... .
Answer:
3xyz

Question 3.
The sum of 8x² + 2x and 4x + 2 is .................. .
Answer:
8x² + 6x + 2

Question 4.
The product of 2x, 4x and \(\frac{2}{3}\)x is ................. .
Answer:
\(\frac{16}{3}\)x³

Question 5.
If x = 1 and y = 2 then the value of 3x² + 4x + 2xy + 2y² is .................. .
Answer:
19

Very Short Answer Type Questions

Question 1.
Find the coefficient of x² in \(\frac{3}{7}\)x²y².
Answer:
Coefficient of x² in
\(\frac{3}{7}\)x²y² = \(\frac{3}{7}\)y²

Question 2.
Write the total number of terms in 5xy + 2xz + 3xy + x² + y².
Answer:
5xy + 2xz + 3xy + x² + y²
= 5xy + 3xy + 2xz + x² + y²
= 8xy + 2xz + x² + y²
No. of terms = 4

Question 3.
Find the sum of \(\frac{5}{6}\)x + \(\frac{7}{6}\)x + \(\frac{1}{6}\)x.
Answer:
\(\frac{5 x+7 x+x}{6}=\frac{13}{6}\) x

Question 4.
Find the sum of (2x + 7), (4x - 2) and (6x + 4).
Answer:
12x + 9

Question 5.
Find the product of (x² + 2x) and (2x + 3).
Answer:
(x² + 2x) (2x +.3)
= x² (2x + 3) + 2x (2x + 3)
= x² × 2x + x² × 3 + 2x × 2x + 2x × 3
= 2x³ + 3x² + 4x² + 6x
= 2x³ + 7x² + 6x

Question 6.
If x = 5, y = 2 then find the value of 3x² + 4xy + 2y².
Answer:
3x² + 4xy + 2y²
= 3 (5)² + 4(5) (2) + 2(2)²
= 3 × 25 + 40 + 2 × 4
= 75 + 40 + 8
= 123

Question 7.
If x = \(\frac{1}{2}\), y = \(\frac{2}{3}\) and z = \(\frac{1}{3}\) then find the value of \(\frac{1}{8}\)xyz.
Answer:
\(\frac{1}{8}\)xyz = \(\frac{1}{8} \times \frac{1}{2} \times \frac{2}{3} \times \frac{1}{3}\)
= \(\frac{1}{8 \times 3 \times 3}\) = \(\frac{1}{72}\)

Question 8.
Define identity.
Answer:
An identity is an equality, which is true for all values of the variables in the equality.

Short Answer Type Questions

Question 1.
By using identity (x + a) (x + b) = x² + (a + b) x + ab find the value of 201 × 202
Answer:
201 × 202 = (200 + 1) × (200 + 2)
= (200)² + [1 + 2] × 200 + 1 × 2
= 40000 + 600 + 2
= 40602

Question 2.
By using identity find the value of (1.2)² - (0.8)2²
Answer:
(1.2)² - (0.8)²
By using identity a² - b² = (a - b) (a + b)
= (1.2 - 0.8) (1.2 + 0.8)
= 0.4 × 2.0 = 0.4 × 2
= 0.8