Question

factorise 1)81p^7-p^3q^4
2)4(x-y)^2-(x+y)^2​

Answer 1

Solution :

81p⁷ - p³q⁴

> p³ ( 81 p⁴ - q⁴ )

> p³ [ ( 9p² )² - ( q²)² ]

> p ³ [ 9p² + q² ][ 9p² - q² ]

> p ³ [ 9p² + q² ][ 3p + q ][ 3p - q]

4(x-y)² - (x+y)²

> 4( x² - 2xy + y² ) - ( x² + 2xy + y²)

> 4x² - 8xy + 4y² - x² - 2xy - y²

> 3x² - 6xy + 3y²

> 3( x² - 2xy + y²)

> 3( x - y)² .

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(a + b)² = a² + 2ab + b²  

(a + b)² = (a - b)² + 4ab  

(a - b)² = a² - 2ab + b²  

(a - b)² = (a + b)² - 4ab  

a² + b² = (a + b)² - 2ab  

a² + b² = (a - b)² + 2ab  

2 (a² + b²) = (a + b)² + (a - b)²

4ab = (a + b)² - (a - b)²  

ab = {(a + b)/2}² - {(a-b)/2}²

(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)  

(a + b)³ = a³ + 3a²b + 3ab² b³

(a + b)³ = a³ + b³ + 3ab(a + b)  

(a - b)³ = a³ - 3a²b + 3ab² - b³

a³ + b³ = (a + b)( a² - ab + b² )

a³ + b³ = (a + b)³ - 3ab( a + b)

a³ - b³ = (a - b)( a² + ab + b²)

a³ - b³ = (a - b)³ + 3ab ( a - b )

Answer 2

Step-by-step explanation:

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1) 81p⁷-p³q⁴

p³(81p⁴-q⁴)

p³[(9p)²-(q²)²]

p³[(9p+q²)(9p-q²)]