Factorization of p² − 2p − (q + 1)(q − 1) is: 1. (p + q − 1)(p − q + 1) 2. (p − q + 1)(p − q − 1) 3. (p + q − 1)(p − q − 1) 4. (p + q + 1)(p − q)

Given, ⇒ p2 − 2p − (q + 1)(q − 1) ⇒ p2 − 2p − (q2 - 1) ⇒ p2 − 2p − q2 + 1 ⇒ p2 − 2p + 1 − q2 ⇒ (p - 1)2 − q2 ⇒ (p - 1 + q)(p - 1 - q) ⇒ (p + q − 1)(p − q - 1). Hence, option 3 is correct option.

Mathematics

Factorization of p² − 2p − (q + 1)(q − 1) is:
(p + q − 1)(p − q + 1)
(p − q + 1)(p − q − 1)
(p + q − 1)(p − q − 1)
(p + q + 1)(p − q)

Factorisation

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Answer

Given,

⇒ p² − 2p − (q + 1)(q − 1)

⇒ p² − 2p − (q² - 1)

⇒ p² − 2p − q² + 1

⇒ p² − 2p + 1 − q²

⇒ (p - 1)² − q²

⇒ (p - 1 + q)(p - 1 - q)

⇒ (p + q − 1)(p − q - 1).

Hence, option 3 is correct option.

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Mathematics

Factorization of p² − 2p − (q + 1)(q − 1) is:
(p + q − 1)(p − q + 1)
(p − q + 1)(p − q − 1)
(p + q − 1)(p − q − 1)
(p + q + 1)(p − q)

Factorisation

Answer

Related Questions

1 − x⁹ = (1 − x)(1 + x + x²) ……………
1 − x³ + x⁶
1 + x³ + x⁶
1 − x³ − x⁶
1 + x³ − x⁶

7 − 12m − 4m² =
(1 − 2m)(7 + 2m)
(1 + 2m)(7 − 2m)
(1 + 2m)(7 + 2m)
(2m − 1)(7 + 2m)

Assertion(A): One of the factors of (5x + 1)² + (25x² - 1) is 2x.
Reason(R): (a + b)² = (a + b)(a + b) and a² - b² = (a + b)(a - b)
A is true, R is false
A is false, R is true
Both A and R are true
Both A and R are false

Mathematics

Factorization of p2 − 2p − (q + 1)(q − 1) is:(p + q − 1)(p − q + 1)(p − q + 1)(p − q − 1)(p + q − 1)(p − q − 1)(p + q + 1)(p − q)

Factorisation

Answer

Related Questions

1 − x9 = (1 − x)(1 + x + x2) ……………1 − x3 + x61 + x3 + x61 − x3 − x61 + x3 − x6

7 − 12m − 4m2 =(1 − 2m)(7 + 2m)(1 + 2m)(7 − 2m)(1 + 2m)(7 + 2m)(2m − 1)(7 + 2m)

Assertion(A): One of the factors of (5x + 1)2 + (25x2 - 1) is 2x.Reason(R): (a + b)2 = (a + b)(a + b) and a2 - b2 = (a + b)(a - b)A is true, R is falseA is false, R is trueBoth A and R are trueBoth A and R are false

Factorization of p² − 2p − (q + 1)(q − 1) is:
(p + q − 1)(p − q + 1)
(p − q + 1)(p − q − 1)
(p + q − 1)(p − q − 1)
(p + q + 1)(p − q)

1 − x⁹ = (1 − x)(1 + x + x²) ……………
1 − x³ + x⁶
1 + x³ + x⁶
1 − x³ − x⁶
1 + x³ − x⁶

7 − 12m − 4m² =
(1 − 2m)(7 + 2m)
(1 + 2m)(7 − 2m)
(1 + 2m)(7 + 2m)
(2m − 1)(7 + 2m)

Assertion(A): One of the factors of (5x + 1)² + (25x² - 1) is 2x.
Reason(R): (a + b)² = (a + b)(a + b) and a² - b² = (a + b)(a - b)
A is true, R is false
A is false, R is true
Both A and R are true
Both A and R are false