Question 3 :
If $a\, -\displaystyle \frac{1}{a}\, =\, 8$ and $a\, \neq\, 0$; find $a^{2}\, -\, \displaystyle \frac{1}{a^{2}}$
Question 8 :
State whether the statement is True or False.Expand: $(2a+b)^2 $ is equal to $4a^2+4ab+b^2$.<br/>
Question 9 :
State whether the statement is True or False.Evaluate: $(2a+3)(2a-3)(4a^2+9)$ is equal to $16a^4-81$.<br/>
Question 11 :
Use the product $ (a+b)(a-b) = a^2-b^2$ to evaluate:<br>$21\times 19 $
Question 12 :
If $x + \displaystyle \frac{1}{x} = a+ b$ and $x - \displaystyle \frac{1}{x} = a - b$, then
Question 13 :
State whether the statement is True or False.Expand: $(2x-\dfrac{1}{2x})^2 $ is equal to $4x^2-2+\dfrac{1}{4x^2} $.<br/>
Question 15 :
If $x+\dfrac { 1 }{ x } =3$, then ${ x }^{ 4 }+\dfrac { 1 }{ x^{ 4 } }$=
Question 16 :
State whether the statement is True or False.$\left(3x-\dfrac{1}{2y}\right)\left(3x+\dfrac{1}{2y}\right)$ is equal to $9x^2-\dfrac{1}{4y^2}$.<br/>
Question 19 :
If $\displaystyle x \neq 0$, $\displaystyle x + \dfrac{1}{2x} = p$ and $\displaystyle x - \dfrac{1}{2x} = q$; find a relation between $\displaystyle p$ and $\displaystyle q$.
Question 20 :
If $x+y = 9$ and $xy = 16$ , find the value of $(x^2 + y^2)$.
Question 21 :
Solve: $\displaystyle \left ( x-4 \right )^{2}-\left ( x+4 \right )^{2}=48$.
Question 25 :
If $3a = 4b = 6c$ and $a + b + c = 27 \displaystyle \sqrt{29}$, then $\displaystyle \sqrt{a^{2}+b^{2}+c^{2}}$ is 
Question 32 :
Two numbers are such that their sum multiplied by the sum of their squares is $5500$ and their difference multiplied by the difference of the squares is $352$. Then the numbers are ?<br/>
Question 33 :
If $x+y=a $ and $xy=b$, then the value of $\displaystyle \frac{1}{x^{3}}+\frac{1}{y^{3}} $ is
