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Question (11)

QN0029383

Which of the following is equal to (4a − 3b)(4a + 3b)?

(A) 16a² + 9b²
(B) 16a² − 9b²
(C) 8a² − 6b²
(D) 16a² − 24ab + 9b²

Correct Answer: B

Explanation:

Use the identity (a + b)(a − b) = a² − b². Here, (4a)² − (3b)² = 16a² − 9b².

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Question (12)

QN0029384

The value of 104² is

(A) 10806
(B) 10816
(C) 10616
(D) 11016

Correct Answer: B

Explanation:

Use (100 + 4)² = 100² + 2 × 100 × 4 + 4² = 10000 + 800 + 16 = 10816.

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Question (13)

QN0029385

Which expression is equivalent to 6x(x − 4 + y)?

(A) 6x² − 24 + 6xy
(B) 6x² − 24x + 6xy
(C) 6x² − 4x + 6xy
(D) 6x² + 24x + 6xy

Correct Answer: B

Explanation:

Apply the distributive property: 6x × x − 6x × 4 + 6x × y = 6x² − 24x + 6xy.

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Question (14)

QN0029386

A number is multiplied by 101. Which expression represents the distributive property used?

(A) n × 100 − 1
(B) n(100 + 1)
(C) n(99 + 2)
(D) n(50 + 51)

Correct Answer: B

Explanation:

Since 101 = 100 + 1, n × 101 = n(100 + 1) = 100n + n.

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Question (15)

QN0029387

The simplified form of (5m − 2)(5m − 2) is

(A) 25m² − 20m + 4
(B) 25m² − 10m + 4
(C) 25m² + 20m + 4
(D) 25m² − 4

Correct Answer: A

Explanation:

Use (a − b)² = a² − 2ab + b². Thus, (5m − 2)² = 25m² − 20m + 4.

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Question (16)

QN0029388

The value of 995 × 1005 is

(A) 999975
(B) 999025
(C) 1000000
(D) 1000025

Correct Answer: A

Explanation:

Use (1000 − 5)(1000 + 5) = 1000² − 5² = 1000000 − 25 = 999975.

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Question (17)

QN0029389

Which statement is always true?

(A) (a + b)² = a² + b²
(B) (a − b)² = a² − b²
(C) 2(a² + b²) = (a + b)² + (a − b)²
(D) a² − b² = (a − b)²

Correct Answer: C

Explanation:

Expanding both squares gives (a + b)² + (a − b)² = 2a² + 2b² = 2(a² + b²).

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Question (18)

QN0029390

If a = 25 and b = 24, then the increase in the product when both numbers are increased by 1 is

(A) 48
(B) 49
(C) 50
(D) 51

Correct Answer: C

Explanation:

Increase = a + b + 1 = 25 + 24 + 1 = 50.

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Question (19)

QN0029391

Which of the following expressions is correctly expanded?

(A) (2p + 3)(p − 4) = 2p² − 5p − 12
(B) (2p + 3)(p − 4) = 2p² − 8p + 3p − 12 = 2p² − 5p − 12
(C) (2p + 3)(p − 4) = 2p² − 8p + 12
(D) (2p + 3)(p − 4) = 2p² + 5p − 12

Correct Answer: B

Explanation:

Multiply each term: 2p × p = 2p², 2p × (−4) = −8p, 3 × p = 3p, 3 × (−4) = −12. Combine like terms.

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Question (20)

QN0029392

A square has side (x + 6) cm. Which expression represents its area?

(A) x² + 12x + 36
(B) x² + 6x + 36
(C) x² + 36
(D) 2x² + 36

Correct Answer: A

Explanation:

Area = (x + 6)² = x² + 2 × x × 6 + 6² = x² + 12x + 36.

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Question (11)

Which of the following is equal to (4a − 3b)(4a + 3b)?

Explanation:

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Question (12)

The value of 104² is

Explanation:

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Question (13)

Which expression is equivalent to 6x(x − 4 + y)?

Explanation:

Link:

Question (14)

A number is multiplied by 101. Which expression represents the distributive property used?

Explanation:

Link:

Question (15)

The simplified form of (5m − 2)(5m − 2) is

Explanation:

Link:

Question (16)

The value of 995 × 1005 is

Explanation:

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Question (17)

Which statement is always true?

Explanation:

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Question (18)

If a = 25 and b = 24, then the increase in the product when both numbers are increased by 1 is

Explanation:

Link:

Question (19)

Which of the following expressions is correctly expanded?

Explanation:

Link:

Question (20)

A square has side (x + 6) cm. Which expression represents its area?

Explanation:

Link:

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