Algebraic Identity 3

Q.

Verify that : $x^3+y^3+z^3-3xyz=\frac{1}{2}(x+y+z)[{(x-y)}^2+{(y-z)}^2+{(z-x)}^2)]$

Q.

The expansion of $x^3$+$y^3$+$z^3$-3xyz is

1. (x+y+z) (x²+y²+z²+xy+yz+xz)

2. (x+y+z) (x²+y²+z²-xy-yz+xz)

3. (x+y+z) (-yz-xz+x²+y²-xy+z²)
   

4. (x+y+z) (xy+yz+xz-x²-y²-z²)

Q.

If $a+b=10$ and $a-b=4,$ find the value of $a^2-b^2$

1. $35$

2. $40$

3. $30$

4. $45$

Q. Expansion of $(x+y-z{)}^2$ :

1. $x^2+y^2+z^2-2(xy+yz+zx)$
2. $x^2+y^2+z^2+2(xy+yz+zx)$
3. $x^2+y^2+z^2+2(xy-yz-zx)$
4. $x^2+y^2+z^2-2(xy-yz+zx)$

Q.

The difference and product of two numbers is 10 and 20 respectively. Find the difference of their squares.

1. 120

2. 140

3. 100

4. 80

Q. Expansion of $(x+y+z{)}^2$ :

1. $x^2+y^2+z^2+2(xy+yz+zx)$
2. $x^2+y^2+z^2-2(xy+yz+zx)$
3. $x^2+y^2+z^2-2(xy-yz+zx)$
4. $x^2+y^2+z^2+2(xy-yz+zx)$

Q. Which of the following identity can be used to solve 1001 $\times$ 999?

1. $(a+b)\times (a-b)=a^2$ - $b^2$
2. ${(a+b)}^2$ = $a^2$ + $2ab$ + $b^2$
3. $(x+y{)}^3$ = $x^3$ + 3$x^2$$y$ + 3$x$$y^2$ + $y^3$
4. ${(a-b)}^2$ = $a^2$ -$2ab$ + $b^2$

Q. Fill in the blanks:
If $(100{)}^0={10}^n$ then the value of $n$ is ........

Q.

If the value of $a^2+b^2$ = 41 and ab = 20, find the value of a-b

1. 1

2. 2

3. 3

4. 0