Application of Identity: (x+y)^2

Q. Find the relation between $a$ and $b$ by simplifying the expression $(3a+2b{)}^2+(2a+3b{)}^2$.

Also, find the value of expression when $a^2+b^2=5$ and $ab=2$.

1. $113$
2. $13(a^2+b^2)+24ab$
3. $24(a^2+b^2)+13ab$
4. $146$

Q. Find the value of expression $36x^2+64y^2+96xy$, When $x=\frac{2}{3}$ and $y=\frac{3}{4}$.

1. $100$
2. $10$
3. $1000$
4. $50$

Q. The value of $(101{)}^2$ is

1. 10, 200
2. 10, 201
3. 10, 202
4. 10, 203

Q. ${25}^2$ can be expanded and expressed as:

1. $(20+5{)}^2$
   ${20}^2+5^2$
2. $(20+5{)}^2$
   ${20}^2+5^2+20\times 5$
3. $(20+5{)}^2$
   ${20}^2+5^2+2\times 20\times 5$

Q. If $x+y=7$ and $xy=10$, then the value of $\frac{(x^2+y^2)}{2xy+9}$ will be

Q. The value of $(111{)}^2$ is

Q. If $x+y=3$ and $xy=6$, what is the value of the expression $(x^2+y^2{)}^2+4x^2{y}^2+4x{y}^2+4x^{2}y$

1. $36$
2. $45$
3. $81$
4. $72$