Question

Áp dụng bằng hằng đẳng thức đáng nhớ để thực hiện phép chia :

a) \(\left(x^2+2xy+y^2\right):\left(x+y\right)\)

b) \(\left(125x^3+1\right):\left(5x+1\right)\)

c) \(\left(x^2-2xy+y^2\right):\left(y-x\right)\)

Answer 1

a) (x² + 2xy + y²) : (x + y) = (x + y)² : (x + y) = x + y.

b) (125x³ + 1) : (5x + 1) = [(5x)³ + 1] : (5x + 1)

= (5x)² – 5x + 1 = 25x² – 5x + 1.

c) (x² – 2xy + y²) : (y – x) = (x – y)² : [-(x – y)] = - (x – y) = y – x

Hoặc (x² – 2xy + y²) : (y – x) = (y² – 2xy + x²) : (y – x)

= (y – x)² : (y – x) = y - x.

Answer 2

Bài giải:

a) (x² + 2xy + y²) : (x + y) = (x + y)² : (x + y) = x + y.

b) (125x³ + 1) : (5x + 1) = [(5x)³ + 1] : (5x + 1)

= (5x)² – 5x + 1 = 25x² – 5x + 1.

c) (x² – 2xy + y²) : (y – x) = (x – y)² : [-(x – y)] = - (x – y) = y – x

Hoặc (x² – 2xy + y²) : (y – x) = (y² – 2xy + x²) : (y – x)

= (y – x)² : (y – x) = y - x.

Answer 3

a) (x² +2xy + y² ) : (x +y)

= (x +y)² : (x +y)

= x + y

b) (125x³ + 1) : (5x + 1)

= (5x + 1)(25x² - 5x + 1) : (5x + 1)

= 25x² - 5x + 1

c) \(\left(x^2-2xy+y^2\right)\left(y-x\right)\)

= \(\left(x-y\right)^2:\left(y-x\right)\)

= \(x-y\)