Question

viết biểu thức sau dới dạng tích 

a/ x^2-2

b/ y^3-13

c/ 2x^2-4

d/ (x-1)^3-(y+1)^3

 

Answer 1

a) \(x^2-2=\left(x-\sqrt{2}\right)\left(x+\sqrt{2}\right)\)

b) \(y^3-13=\left(y-\sqrt{13}\right)\left(y^2+\sqrt{13}y+13\right)\)

c) \(2x^2-4=\left(\sqrt{2}x-2\right)\left(\sqrt{2}x+2\right)\)

d) \(\left(x-1\right)^3-\left(y+1\right)^3=\left(x-1-y-1\right)\left[\left(x-1\right)^2+\left(x-1\right)\left(y+1\right)+\left(y+1\right)^2\right]=\left(x-y-2\right)\left(x^2-2x+1+xy-y+x-1+y^2+2y+1\right)=\left(x-y-2\right)\left(x^2+y^2-x+y+xy+1\right)\)

Answer 2

Answer 3

a. x² - 2

<=> x² - \(\left(\sqrt{2}\right)^2\)

<=> (x - \(\sqrt{2}\))(x + \(\sqrt{2}\))

b. y³ - 13 

<=> y³ - \(\left(\sqrt[3]{13}\right)^3\)

<=> \(\left(y-\sqrt[3]{13}\right)\left[y^2+\sqrt[3]{13}y+\left(\sqrt[3]{13}\right)^2\right]\)

c. 2x² - 4

<=> \(\left(x\sqrt{2}\right)^2\) - 2²

<=> \(\left(x\sqrt{2}-2\right)\left(x\sqrt{2}+2\right)\)

d. (x - 1)³ - (y + 1)³

\(\Leftrightarrow\left[\left(x-1\right)-\left(y+1\right)\right]\left[\left(x-1\right)^2+\left(x-1\right)\left(y+1\right)+\left(y+1\right)^2\right]\)

\(\Leftrightarrow\left(x-1-y-1\right)\left[\left(x-1\right)^2+\left(x-1\right)\left(y+1\right)+\left(y+1\right)^2\right]\)

\(\Leftrightarrow\left(x-y-2\right)\left[\left(x-1\right)^2+\left(x-1\right)\left(y+1\right)+\left(y+1\right)^2\right]\)

Answer 4

a: \(x^2-2=\left(x-\sqrt{2}\right)\left(x+\sqrt{2}\right)\)

b:\(2x^2-4=2\left(x^2-2\right)=2\left(x-\sqrt{2}\right)\left(x+\sqrt{2}\right)\)

d: \(\left(x-1\right)^3-\left(y+1\right)^3\)

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

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