Algebraic Identities and Number Systems

Factorize  $8x^3+y^3+27z^3-18xyz$  using Identities

•  $\left(2x+y+3z\right)\left(4x^2+y^2+9z^2-2xy-3yz-6xz\right)$  

•  $\left(x-y+3z\right)\left(2x^2+2y^2-3z^2-2xy+3zy-4xz\right)$  

•  $\left(2x+y-z\right)\left(3x^2+y^2-9z^2-xy-yz-zx\right)$  

Factorize using identities  $4x^2+9y^2+16z^2+12xy-24yz-16xz$  

•  $\left(4x+2y-3z\right)\left(3x+4y-2z\right)$  

•  $\left(4x-y+3z\right)\left(3x+2y-4z\right)$  

•  $\left(2x+3y-4z\right)\left(2x+3y-4z\right)$  

Factorize using identities -  $8a^3+b^3+12a^2b+6ab^2$  

•  $\left(2a+b+ab\right)\left(2a+b\right)$  

•  $\left(2a+b\right)\left(2a-b\right)\left(2a+b\right)$  

•  $\left(2a+b\right)\left(2a+b\right)\left(2a+b\right)$  

 $x^2+\frac{1}{x^{2\ }}=102,\ then\ x-\frac{1}{x}=?$  

• 8

• 10

• 12

• 13

 $If\ a+b+c=9\ and\ ab+bc+ca=23,\ then\ a^2+b^2+c^2\ =?$  

• 35

• 58

• 127

• 153

 $If\ \frac{a}{b}+\frac{b}{a}=-1,\ then\ a^3-b^3=?$  

• 1

• -1

• 1/2

• 0 

 $\left(x-y\right)\left(x+y\right)\left(x^2+y^2\right)\left(x^4+y^4\right)=?$  

•  $x^{16}-y^{16}$  

•  $x^8-y^8$  

•  $x^8+y^8$  

•  $x^{16}+y^{16}$  

 $\left(\sqrt{3\ }+\sqrt{5}\right)\left(\sqrt{2\ }+\sqrt{3}\right)$  How many Irrational expressions are present in the expansion of this expression?

• 1

• 2

• 3

• 4

The Height of a building is 564 meters. It has 2013 steps to reach the top. The height of each step would be

• Irrational number

• Rational number

• Integer

• Whole number

Which of the following bags contains more numbers?

• Bag containing all integers between 1 and 1,00,00,000

• Bag containing rational numbers between 1 and 3

• A bag containing all integers between -10,00,000 and 10,00,000