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Maths Quiz for Class 8 Standard Identities |
In this post, we are providing 20 online maths quiz
questions for class 8 standard identities. Online maths quiz will take around
20 minutes to complete it.
Question 1: Which of the following is a correct standard identity?
A) (a
+ b)2 = a2 – 2ab
+ b2
B) (a
– b)2 = a2 – 2ab
– b2
C) (a
+ b) (a – b) = a2
– b2
D) (a
+ b) (a – b) = 2a – 2b
Explanation: (a
+ b) (a – b) = a2
– b2 is the correct standard identity.
Question 2: (x + a) (x + b) = _________________
A) x2 + (a + b)x + ab
B) a2 – 2ab + b2
C) a2 + 2ab + b2
D) a2 – b2
Explanation: (x + a) (x + b) = x2 + (a + b)x + ab
Question 3: Expand (2x + 3y)2 using (a + b)2 = a2 + 2ab + b2.
A) 4x2 + 12xy + 9y2
B) 2x2 + 12xy + 3y2
C) 4x2 + 4xy + 9y2
D) 4x2 + 6xy + 9y2
Explanation: We know that (a + b)2 = a2 + 2ab + b2. Therefore, (2x + 3y)2 = (2x)2 + 2(2x)(3y) + (3y)2 = 4x2 + 12xy + 9y2
Question 4: Expand (5x – 4y)2 using (a – b)2 = a2 – 2ab + b2.
A) 5x2 – 40xy + 4y2
B) 25x2 – 40xy + 16y2
C) 25x2 + 40xy + 16y2
D) 25x2 – 20xy + 16y2
Explanation: We know that (a – b)2 = a2 – 2ab + b2. Therefore, (5x – 4y)2 = (5x)2 – 2(5x)(4y) + (4y)2 = 25x2 – 40xy + 16y2
Question 5: Expand (7x + 2y) (7x – 2y) using (a + b) (a – b) = a2 – b2.
A) 7x2 – 2y2
B) 49x2 – 4y2
C) 49x2 + 4y2
D) 14x2 – 4y2
Explanation: We know that (a + b) (a – b) = a2 – b2. Therefore, (7x + 2y) (7x – 2y) = (7x)2 – (2y)2 = 49x2 – 4y2
Question 6: Expand (a/2 + 8b)2 using (a + b)2 = a2 + 2ab + b2.
A) a2/4 + 8ab + 8b2
B) a2/4 + 16ab + 64b2
C) a2/4 + 8ab + 64b2
D) a2/2 + 8ab + 64b2
Explanation: We know that (a + b)2 = a2 + 2ab + b2. Therefore, (a/2 + 8b)2 = (a/2)2 + 2(a/2)(8b) + (8b)2 = a2/4 + 8ab + 64b2
Question 7: Expand (p/3 – 6q)2 using (a – b)2 = a2 – 2ab + b2.
A) p2/9 – 6pq + 36q2
B) p2/9 – 4pq + 36q2
C) p2/9 – 12pq + 36q2
D) p2/9 – 18pq + 36q2
Explanation: We know that (a – b)2 = a2 – 2ab + b2. Therefore, (p/3 – 6q)2 = (p/3)2 – 2(p/3)(6q) + (6q)2 = p2/9 – 4pq + 36q2
Question 8: Expand (a/5 + 3b) (a/5 – 3b) using (a + b) (a – b) = a2 – b2.
A) a2/5 – 3b2
B) a2/5 – 9b2
C) a2/25 + 9b2
D) a2/25 – 9b2
Explanation: We know that (a + b) (a – b) = a2 – b2. Therefore, (a/5 + 3b) (a/5 – 3b) = (a/5)2 – (3b)2 = a2/25 – 9b2
Question 9: Expand (x + 5) (x + 7) using (x + a) (x + b) = x2 + (a + b)x + ab.
A) x2 + 12x + 35
B) x2 + 35x + 12
C) x2 – 12x + 35
D) x2 + 12x – 35
Explanation: We know that (x + a) (x + b) = x2 + (a + b)x + ab. Therefore, (x + 5) (x + 7) = x2 + (5 + 7)x + 5 × 7 = x2 + 12x + 35.
Question 10: Expand (x + 2) (x – 3) using (x + a) (x + b) = x2 + (a + b)x + ab
A) x2 – x + 6
B) x2 + 5x – 6
C) x2 – x – 6
D) x2 + x – 6
Explanation: We know that (x + a) (x + b) = x2 + (a + b)x + ab. Therefore, (x + 2) (x – 3) = x2 + (2 – 3)x + 2 × (–3) = x2 – x – 6.
Question 11: Expand (x – 5) (x + 8) using (x + a) (x + b) = x2 + (a + b)x + ab
A) x2 + 13x – 40
B) x2 + 3x – 40
C) x2 + 3x + 40
D) x2 – 3x – 40
Explanation: We know that (x + a) (x + b) = x2 + (a + b)x + ab. Therefore, (x – 5) (x + 8) = x2 + (–5 + 8)x + (–5) × 8 = x2 + 3x – 40.
Question 12: Expand (x – 6) (x – 4) using (x + a) (x + b) = x2 + (a + b)x + ab
A) x2 + 10x + 24
B) x2 – 10x + 24
C) x2 – 2x + 24
D) x2 + 2x + 24
Explanation: We know that (x + a) (x + b) = x2 + (a + b)x + ab. Therefore, (x – 6) (x – 4) = x2 + (–6 – 4)x + (–6) × (–4) = x2 – 10x + 24.
Question 13: Expand (4x + 5) (4x + 6) using (x + a) (x + b) = x2 + (a + b)x + ab
A) 16x2 + 44x + 30
B) 16x2 + 11x + 30
C) 16x2 – 11x + 30
D) 16x2 – 44x + 30
Explanation: We know that (x + a) (x + b) = x2 + (a + b)x + ab. Therefore, (4x + 5) (4x + 6) = (4x)2 + (5 + 6)4x + 5 × 6 = 16x2 + 44x + 30.
Question 14: Expand (2x – 3) (2x – 5) using (x + a) (x + b) = x2 + (a + b)x + ab
A) 4x2 – 8x + 15
B) 4x2 + 16x + 15
C) 4x2 – 16x – 15
D) 4x2 – 16x + 15
Explanation: We know that (x + a) (x + b) = x2 + (a + b)x + ab. Therefore, (2x – 3) (2x – 5) = (2x)2 + (–3 – 5)2x + (–3) × (–5) = 4x2 – 16x + 15.
Question 15: Evaluate (205)2 using (a + b)2 = a2 + 2ab + b2.
A) 4225
B) 40225
C) 42025
D) 41025
Explanation: We know that (a + b)2 = a2 + 2ab + b2. Therefore, (205)2 = (200 + 5)2 = (200)2 + 2(200)(5) + (5)2 = 40000 + 2000 + 25 = 42025
Question 16: Evaluate (996)2 using (a – b)2 = a2 – 2ab + b2.
A) 99216
B) 992016
C) 982016
D) 991016
Explanation: We know that (a – b)2 = a2 – 2ab + b2. Therefore, (996)2 = (1000 – 4)2 = (1000)2 – 2(1000)(4) + (4)2 = 1000000 – 8000 + 16 = 992016
Question 17: Evaluate 510 × 490 using (a + b) (a – b) = a2 – b2.
A) 249900
B) 249000
C) 249800
D) 259900
Explanation: We know that (a + b) (a – b) = a2 – b2. Therefore, 510 × 490 = (500 + 10) (500 – 10) = (500)2 – (10)2 = 250000 – 100 = 249900
Question 18: Evaluate (408)2 using (a + b)2 = a2 + 2ab + b2.
A) 160464
B) 1660464
C) 166464
D) 166064
Explanation: We know that (a + b)2 = a2 + 2ab + b2. Therefore, (408)2 = (400 + 8)2 = (400)2 + 2(400)(8) + (8)2 = 160000 + 6400 + 64 = 166464
Question 19: Evaluate (296)2 using (a – b)2 = a2 – 2ab + b2.
A) 87016
B) 87616
C) 870616
D) 87600
Explanation: We know that (a – b)2 = a2 – 2ab + b2. Therefore, (296)2 = (300 – 4)2 = (300)2 – 2(300)(4) + (4)2 = 90000 – 2400 + 16 = 87616
Question 20: Evaluate 1005 × 995 using (a + b) (a – b) = a2 – b2.
A) 9999975
B) 99975
C) 999975
D) 999925
Explanation: We know that (a + b) (a – b) = a2 – b2. Therefore, 1005 × 995 = (1000 + 5) (1000 – 5) = (1000)2 – (5)2 = 1000000 – 25 = 999975
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