Question

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

a) (x² + 2xy + y²) : (x + y);                       b) (125x³ + 1) : (5x + 1);

c) (x² – 2xy + y²) : (y – x).

 

Answer 1

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

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

\(=\left(x+y\right)\)

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

\(=\left[\left(5x\right)^3+1\right]:\left(5x+1\right)\)

\(=\left(5x\right)^2-5x+1\)

\(=25x^2-5x+1\)

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

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

\(=-\left(x-y\right)\)

\(=y-x\)

Answer 2

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

b) \(\left(125x^3+1\right)\left(5x+1\right)\\=\left[\left(5x\right)^3+1\right]:\left(5x+1\right)\\ =\left(5x\right)^2-5x+1 \\ =25x^2-5x+1\)

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