Deducing Formula for (x+y)^2

Q. Find the value of${102}^2$ using a suitable algebraic identity.

1. 10404
2. 10202
3. 10101
4. 10606

Q.

Using identities, evaluate ${102}^2$.

Q. Find the value of $9.7\times 9.8$ using a suitable algebraic identity.

1. 95.06
2. 96.42
3. 94.56
4. 95.26

Q.

The square of $20\frac{1}{2}$ is equal to

1. 422.50

2. 415.75

3. 424.25

4. 420.25

Q.

${\left(\frac{a}{4}-\frac{b}{2}+1\right)}^2$expand it with suitable identities .

Q.

If $(a+b)=6$, and $ab=2$, then the value of $\frac{1}{a^2}+\frac{1}{b^2}$ is equal to

1. 8

2. 12

3. 16

4. 4

Q. Find the square of number $39$ without actual multiplication.

1. $1521$
2. $1625$
3. $1574$
4. $1624$

Q.

The square of 10.2 is equal to

1. 102.02

2. 104.04

3. 104.02

4. 102.04

Q.

Addition of expression $5\sqrt{3}-2\sqrt{7}$ and $2\sqrt{3}+\sqrt{5}$ is

1. $5\sqrt{3}-2\sqrt{7}+2\sqrt{3}+\sqrt{5}$

2. $10\sqrt{6}-2\sqrt{7}+\sqrt{5}$

3. $7\sqrt{3}-2\sqrt{7}+\sqrt{5}$

4. None of these

Q. $\text{Find the value of}{23}^2\text{by using identities.}$

Q. If ${35}^2$ is 1225 and the difference between 35 and 25 is 10. Difference between 50 and 35 is 15 and ${15}^2$ is 225 .So we will use the method of finding square between 75 and 125 or not?

Q.

The value of ${44}^2$ is equal to

1. $1836$

2. $1936$

3. $1816$

4. $1916$

Q.

The value of ${12}^4$ calculated using binomial expansion is

1. 20734

2. 20736

3. 20732

4. 20738

Q.

The square of $20\frac{1}{5}$ is equal to ____

1. $408\frac{1}{25}$

2. 408
3. None of the above

4. $408\frac{25}{1}$

Q.

Question 86 (viii)

Using suitable identities, evaluate the following:

$52\times 53$

Q. If $(a+b)=6$, and $ab=2$, then the value of $\frac{1}{a^2}+\frac{1}{b^2}$ is equal to

Q. If $a^2+\frac{1}{a^2}=23$, then find $a+\frac{1}{a}$.

1. 20
2. 25
3. 5
4. 4

Q. Which of the following is the correct expansion of $(2a+b{)}^2$?

1. $a^2+b^2+ab$
2. $2a^2+b^2+2ab$
3. $4a^2+b^2+4ab$
4. $a^2+b^2+2ab$

Q. If the value of $\left(\frac{a^3-b^3}{a^3+b^3}\right)$ when a = 7 and b = 2 is $\frac{335}{p}$, then find the value of p.

Q.

The expansion $(x+a)(x+b)$ is

1. $x^2+(a-b)x+ab$
2. $x^2+(a+b)x+ab$
3. $x^2-(a+b)x+ab$
4. $x^2+(a+b)x-ab$

Q.

Question 70

In the following question, state whether the given statements are true (T) or false (F).

$329.25=3\times {10}^2+2\times {10}^1+9\times {10}^0+2\times {10}^{-1}+5\times {10}^{-2}$

Q. If the value of $p^2+q^2=21$ and $pq=30$, then find the value of $(p+q{)}^2$. [2 marks]

Q. ${(2x^2+3x+5)}^{1/2}+{(2x^2+3x+20)}^{1/2}=15$ therefore x is

1. (-8/3)
2. (14/5)
3. (-11/2)
4. 4

Q. The value of $(998{)}^2$ is equal to:

1. 9, 96, 016

2. 9, 86, 004

3. 9, 96, 004

4. 9, 93, 004

Q.

Use suitable identity and find the value of ${97}^2$

1. 10409

2. 90409

3. 9409

4. 11049

Q.

The square of $40\frac{1}{4}$ is

1. $810\frac{1}{16}$

2. $1620\frac{1}{4}$

3. $1620\frac{1}{8}$

4. $1620\frac{1}{16}$

Q. Find the square of :
$(2x+\frac{1}{x}+1)$

Q. Question 1(vi)
Use a suitable identity to get each of the following products:
$(a^2+b^2)(-a^2+b^2)$

Q.

The square of 52 is equal to

1. 2704

2. 2814

3. 2714

4. 2724

Q. The square of $\sqrt{5}-2$ is $9-4\sqrt{5}$