Question 1 :
State whether the statement is True or False.Expand: $(a-2b)^2 $ is equal to $a^2-4ab+4b^2$.<br/>
Question 2 :
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 4 :
If $x + \displaystyle \frac{1}{x} = a+ b$ and $x - \displaystyle \frac{1}{x} = a - b$, then
Question 5 :
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 11 :
State whether the statement is True or False.Find the square: $(a+\dfrac{1}{5a})$, then answer is $a^2+1+\dfrac{1}{4a^2}$.<br/>
Question 13 :
State whether the statement is True or False.Expand: $(2a+b)^2 $ is equal to $4a^2+4ab+b^2$.<br/>
Question 14 :
State whether the statement is True or False.Evaluate: $(4x^2-5y^2)(4x^2+5y^2)$ is equal to $16x^4-25y^4$.<br/>
Question 16 :
State whether the statement is True or False.Evaluate: $(a+bc)(a-bc)(a^2+b^2c^2)$ is equal to $a^4-b^4c^4$.<br/>
Question 18 :
If $x+\dfrac { 1 }{ x } =3$, then ${ x }^{ 4 }+\dfrac { 1 }{ x^{ 4 } }$=
Question 20 :
If $x+y = 9$ and $xy = 16$ , find the value of $(x^2 + y^2)$.
Question 22 :
State whether the statement is True or False.Evaluate: $(2a+3)(2a-3)(4a^2+9)$ is equal to $16a^4-81$.<br/>
Question 24 :
$(2x + 3y)^{2} = 4x^{2} + 9y^{2} + M$, find M.<br/>
Question 25 :
If $a\, -\displaystyle \frac{1}{a}\, =\, 8$ and $a\, \neq\, 0$; find $a^{2}\, -\, \displaystyle \frac{1}{a^{2}}$
Question 26 :
$\displaystyle \left ( x-y-z \right )^{2}-\left ( x+y+z \right )^{2}$ is equal to
Question 27 :
Use the product $ (a+b)(a-b) = a^2-b^2$ to evaluate:<br/>$103\times 97 $
Question 28 :
If $\displaystyle a + \dfrac{1}{a} = m$ and $\displaystyle a \neq 0$; find in terms of $\displaystyle 'm'$ ; the value of: $\displaystyle a - \dfrac{1}{a}$
Question 34 :
If $\displaystyle \left (x - \frac{1}{x} \right ) = 5$  find the value of $\displaystyle \left (x^4 + \frac{1}{x^4} \right )$.
Question 35 :
If $\displaystyle a^{2} + b^{2} = 34$ and $\displaystyle ab = 12$; find $\displaystyle 7 \left (a - b \right )^{2} - 2\left (a + b \right )^{2}$<br/>
Question 39 :
State whether the statement is True or False.Evaluate: $(1.6x+0.7y)(1.6x-0.7y)$ is equal to $2.56x^2-0.49y^2$.<br/>
Question 40 :
The product of $(2x^2 -3x + 1)$ and (x -3) is.equal to
Question 42 :
State whether the statement is True or False.Evaluate: $(2x-\dfrac{3}{5})(2x+\dfrac{3}{5})$ is equal to $4x^2-\dfrac{9}{25}$.<br/>
Question 44 :
State whether the statement is True or False.The square of $(x+3y)$ is equal to $x^2+6xy+9y^2$.<br/>
Question 47 :
Simplify the following: <br/>$(\sqrt{3}-\sqrt{2})^{2}$ is equal to $5-2\sqrt{6}$<br/> If true then enter $1$ and if false then enter $0$<br/>
Question 48 :
If $a-b=3$ and $ \displaystyle a^{3}-b^{3}=117 $ then $a+b$ is equal to 
Question 49 :
State whether the statement is True or False.Evaluate: $(6-5xy)(6+5xy)$ is equal to $36-25x^2y^2$.
Question 50 :
If $\displaystyle a+b=7 \ and \ ab=6 \, ,find \ a^{2}-b^{2}$<br/>
Question 51 :
If $\sqrt {x} + \dfrac {1}{\sqrt {x}} =3,$ find the value of $x^{2}+ \dfrac {1}{x^{2}}$  :
Question 53 :
If $\left(y + \dfrac{1}{y}\right) = 12$, then $\left(y^3 + \dfrac{1}{y^3}\right)$ is equal to:-
Question 55 :
How many pairs of natural numbers are there so that difference of the square of the first tois 60 ?<br>(Note : If (a,b) is a pair satisfying , we will not consider (b,a) as a pair)
Question 56 :
If $2x - \dfrac{1}{2x} = 3$, find the value of $16x^4 + \dfrac{1}{16x^4} $
Question 59 :
The difference between two positive numbers is $4$ and difference between their cubes is $316$. Find their product
Question 60 :
If $\displaystyle a + \dfrac{1}{a} = 4$ and $\displaystyle a \neq 0$, find $\displaystyle a^{2} + \dfrac{1}{a^{2}}$.
Question 61 :
Two positive numbers $\displaystyle x$ and $\displaystyle y$ are such that $\displaystyle x > y$. If the difference of these numbers is $\displaystyle 5$ and their product is $\displaystyle 24$, find sum of these numbers<br/>
Question 62 :
If $\displaystyle a \neq 0$ and $\displaystyle a - \dfrac{1}{a} = 4$, find:$\displaystyle a^{4} + \dfrac{1}{a^{4}}$
Question 64 :
The sum of two numbers is 7 and the sum of their cubes is 133, find the sum of their squares.
Question 65 :
Use the product $ (a+b)(a-b) = a^2-b^2$ to evaluate:<br/>$8.3\times 7.7 $<br/>
Question 70 :
State whether the statement is True or False.The square of $(8x+\dfrac{3}{2}y )$ is equal to $64x^2+24xy+\frac{9}{4}y^2 $.<br/>
Question 72 :
State whether the statement is True or False.The square of $(2m^2-\dfrac{2}{3}n^2 )$ is equal to $4m^4-\dfrac{8}{3}m^2n^2+\dfrac{4}{9}n^4$.<br/>
Question 76 :
If $3a = 4b = 6c$ and $a + b + c = 27 \displaystyle \sqrt{29}$, then $\displaystyle \sqrt{a^{2}+b^{2}+c^{2}}$ is 
Question 77 :
Solve: $\displaystyle \left ( x-4 \right )^{2}-\left ( x+4 \right )^{2}=48$.
Question 83 :
If $\displaystyle 2 \left ( x^{2} + 1 \right ) = 5x$, find $\displaystyle x^{3} - \dfrac{1}{x^{3}}$<br/>
Question 84 :
Find the value of 'a' in $4x^{2}\, +\, ax\, +\, 9\, =\, (2x\, -\, 3)^{2}$
Question 85 :
If $\displaystyle \dfrac{x^{2} + 1}{x} = 3\dfrac{1}{3}$ and $\displaystyle x > 1$; find the value of $\displaystyle x^{3} - \dfrac{1}{x^{3}}$
Question 87 :
If $\displaystyle a + \dfrac{1}{a} = 4$ and $\displaystyle a \neq 0$, find :<br/>$\displaystyle a^{4} + \dfrac{1}{a^{4}}$
Question 88 :
If $\displaystyle a + \dfrac{1}{a} = m$ and $\displaystyle a \neq 0$; find in terms of $\displaystyle 'm'$; the value of: $\displaystyle a^{2} - \dfrac{1}{a^{2}}$<br/>
Question 90 :
Using the reals $a_n; \hspace {2mm} (n=1,2,...,5)$, if $l,m,n \in \{1,2,3,4,5\}$ $m < n$.
Question 103 :
If $x+y=a $ and $xy=b$, then the value of $\displaystyle \frac{1}{x^{3}}+\frac{1}{y^{3}} $ is
Question 105 :
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 106 :
Given the polynomial $a_{0}x^{n} + a_{1}x^{n - 1} + ... + a_{n - 1}x + a_{n}$, where $n$ is a positive integer or zero, and $a_{0}$ is a positive integer. The remaining $a's$ are integers or zero. Set$h = n + a_{0} + |a_{1}| + |a_{2}| + .... + |a_{n}|$. The number of polynomials with $h = 3$ is
Question 107 :
The value of$\displaystyle \left ( x-y \right )^{3}+\left ( x+y \right )^{3}+3\left ( x-y \right )^{2}\left ( x+y \right )+3\left ( x+y \right )^{2}\left ( x-y \right )$ is
