Factorise each of the following: (i) 27y³ + 125x³ (ii) 64m³ – 343n³

(i) 27y 3 + 125z 3 [∵ x 3 + y 3 = (x + y)(x 2 - xy + y 2 )] ⇒ 27y 3 + 125z 3 = (3y) 3 + (5z) 3 Putting x = 3y, y = 5z R.H.S = (x + y)(x 2 - xy + y 2 ) = (3y + 5z)[(3y) 2 - (3y)(5z) + (5z) 2 ] = (3y + 5z)(9y 2 - 15yz + 25z 2 ) Hence, 27y 3 + 125z 3 = (3y + 5z)(9y 2 - 15yz + 25z 2 ) (ii) 64m 3 - 343n 3 [∵ a 3 - b 3 = (a - b)(a 2 + ab + b 2 )] ⇒ 64m 3 - 343n 3 = (4m) 3 - (7n) 3 Putting a = 4m, b = 7n R.H.S = (a - b)(a 2 + ab + b 2 ) = (4m - 7n)[(4m) 2 + (4m)(7n) + (7n) 2 ] = (4m - 7n)(16m 2 + 28mn + 49n 2 ) Hence, 64m 3 - 343n 3 = (4m - 7n)(16m 2 + 28mn + 49n 2 )

Mathematics

Factorise each of the following:
(i) 27y³ + 125z³
(ii) 64m³ - 343n³

Polynomials

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Answer

(i) 27y³ + 125z³

[∵ x³ + y³ = (x + y)(x² - xy + y²)]

⇒ 27y³ + 125z³ = (3y)³ + (5z)³

Putting x = 3y, y = 5z

R.H.S = (x + y)(x² - xy + y²)

= (3y + 5z)[(3y)² - (3y)(5z) + (5z)²]

= (3y + 5z)(9y² - 15yz + 25z²)

Hence, 27y³ + 125z³ = (3y + 5z)(9y² - 15yz + 25z²)

(ii) 64m³ - 343n³

[∵ a³ - b³ = (a - b)(a² + ab + b²)]

⇒ 64m³ - 343n³ = (4m)³ - (7n)³

Putting a = 4m, b = 7n

R.H.S = (a - b)(a² + ab + b²)

= (4m - 7n)[(4m)² + (4m)(7n) + (7n)²]

= (4m - 7n)(16m² + 28mn + 49n²)

Hence, 64m³ - 343n³ = (4m - 7n)(16m² + 28mn + 49n²)

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Mathematics

Factorise each of the following:
(i) 27y³ + 125z³
(ii) 64m³ - 343n³

Polynomials

Answer

Related Questions

Verify :
(i) x³ + y³ = (x + y) (x² - xy + y²)
(ii) x³ - y³ = (x - y) (x² + xy + y²)

Factorise : 27x³ + y³ + z³ - 9xyz

Mathematics

Factorise each of the following:(i) 27y3 + 125z3(ii) 64m3 - 343n3

Polynomials

Answer

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Verify :(i) x3 + y3 = (x + y) (x2 - xy + y2)(ii) x3 - y3 = (x - y) (x2 + xy + y2)

Factorise : 27x3 + y3 + z3 - 9xyz

Factorise each of the following:
(i) 27y³ + 125z³
(ii) 64m³ - 343n³

Verify :
(i) x³ + y³ = (x + y) (x² - xy + y²)
(ii) x³ - y³ = (x - y) (x² + xy + y²)

Factorise : 27x³ + y³ + z³ - 9xyz