Question

pttnt a 25x^2-y^2+4y-4

b a^2+b^2-x^2-y^2+2ab-2xy

c 5x^2(x-1)+10xy(x-1)-5y^2(1-x)

d x^5-x^4y-xy^4+y^5

Answer 1

a) 25x² - y² + 4y - 4 

= (5x)² - (y - 2)² 

= (5x + y - 2)(5x - y + 2)

b) a² + b² - x² - y² + 2ab - 2xy 

= (a² + 2ab + b²) - (x² + 2xy + y²)

= (a + b)² - (x + y)²

= (a + b + x + y)(a + b - x - y)

c) 5x²(x - 1) + 10xy(x - 1) - 5y²(1 - x)

= 5x²(x - 1) + 10xy(x - 1) + 5y²(x - 1)

= (x - 1)(5x² + 10xy + 5y²)

= 5(x - 1)(x² + 2xy + y²) 

= 5(x -1)(x  + y)²

d) x⁵ - x⁴y - xy⁴ + y⁵

= x⁴(x - y) - y⁴(x - y)

= (x - y)(x⁴ - y⁴) 

= (x - y)(x² - y²)(x² + y²) = (x - y)²(x + y)(x² + y²) 

Answer 2

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