Algebraic identity for (a+b)^2

Q. If $a^2+\frac{1}{a^2}$ = 23, then the value of $a+\frac{1}{a}$ is equal to .

1. $\pm 2$
2. $\pm 3$
3. $\pm 5$
4. $\pm 7$

Q. $\text{If}(a+\frac{1}{a})=5,$
$\text{then find the value of}(a^2+\frac{1}{a^2}).$

1. 25
2. 23
3. 32
4. 45

Q. $9a^2-\frac{12}{5}a+\frac{4}{25}$ can be expressed as ____.

1. ${(a-\frac{2}{5})}^2$
2. ${(3a-\frac{2}{5})}^2$
3. ${(2a-\frac{2}{5})}^2$
4. ${(a-\frac{5}{2})}^2$

Q.

$\text{Expand:}(x+\frac{1}{x}{)}^2$

1. $x^2-\frac{1}{x^2}+2$

2. $x^2+\frac{1}{x^2}-2$

3. $x^2+\frac{1}{x^2}+2$

4. $x^2+\frac{1}{x}+2$

Q. $\text{If}a=6p\text{and}b=3p,$
$\text{then find the expansion of}$
$(a+b{)}^2+(a-b{)}^2.$

1. $72p^2-18q^2$
2. $72p^2+18q^2$
3. $18p^2+72q^2$
4. $18p^2-72q^2$

Q.

$\text{If}{x}^2+y^2=14\text{and}xy=3,$
then find the value of
$2(x+y{)}^2-5(x-y{)}^2.$

1. 0

2. 106

3. 52

4. 14

Q. Using an identity, find the square of 101.

1. $10201$
2. $10401$
3. $10201$
4. $10204$

Q. $\text{If}(a+\frac{1}{a})=5,$
$\text{then find the value of}(a^2+\frac{1}{a^2}).$

1. 25
2. 23
3. 32
4. 45

Q. $\text{If each side of a square is of length}$
$(x+5)\text{units, then find its area?}$

1. $x^2-25$ sq units
2. $x^2+25$ sq units
3. $x^2-10x+25$ sq units
4. $x^2+10x+25$ sq units