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

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

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

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

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

\(a,=5\sqrt{2}-3\sqrt{2}+\sqrt{2}=3\sqrt{2}\\ b,=\dfrac{\sqrt{3}-\sqrt{2}+\sqrt{3}+\sqrt{2}}{\left(\sqrt{2}+\sqrt{3}\right)\left(\sqrt{3}-\sqrt{2}\right)}=\dfrac{2\sqrt{3}}{3-2}=2\sqrt{3}\)

7/8

1/3

3/7

\(a,\dfrac{7}{8}:b,\dfrac{1}{3}c;\dfrac{3}{7}\)

A)7/8

B)1/3

C)3/7

a.-3/4 < 2/4

b.-8/13 > -12/13

c.-3/7 < 4/5

d.12/-18 = -2/3 

b: =100*100+(24-4)/4