Question

phân tích ĐT sau thành nhân tử

a)x^2-2xy+y^2-1

b)9-x^2-2xy-y^2

c)25-x^2+4xy-4y^2

Answer 1

a) \(x^2-2xy+y^2-1=\left(x-y\right)^2-1=\left(x-y-1\right)\left(x-y+1\right)\)

b) \(9-x^2-2xy-y^2=9-\left(x^2+2xy+y^2\right)=9-\left(x+y\right)^2=\left(3-x-y\right)\left(3+x+y\right)\)

c) \(25-x^2+4xy-4y^2=25-\left(x^2-4xy+4y^2\right)=25-\left(x-2y\right)^2=\left(5-x+2y\right)\left(5+x-2y\right)\)

Answer 2

a. x² - 2xy + y² - 1

= (x - y)² - 1²

= (x - y - 1)(x - y + 1)

b. 9 - x² - 2xy - y²

= 3² - (x + y)²

= (3 - x - y)(3 + x + y)

c. 25 - x² + 4xy - 4y²

= 5² - \(\left[x^2-4xy+\left(2y\right)^2\right]\)

= 5² - (x - 2y)²

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