Algebraic Identity 1

Q.

Evaluate $(102{)}^2$ using suitable identity

1. 4xy

2. 4xz

3. 4xz

4. 4xyz

Q.

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

1. 60

2. 80

3. 100

4. 50

Q. If $2x+3y=13$ and $xy=6$, find the value of $8x^3+21y^3$.

Q.

Use identities to evaluate ${201}^2$

1. 40411

2. 41401

3. 40401

4. 40141

Q.

If $(2x+3y{)}^2=130$ and $xy=6,$ find the value of $4x^2+9y^2$

1. $58$

2. $62$

3. $59$

4. $57$

Q. Use the identity $(x+a)(x+b)=x^2+(a+b)x+ab$ to find the following products:
(xyz-4) (xyz-2)

1. $x^2{y}^2{z}^2-6xyz+8$
2. $x^2{y}^2{z}^2+6x+8$
3. $x^2{y}^2{z}^2-6x-8$
4. $x^2{y}^2{z}^2-6xyz-8$

Q. Match the following with the value of $a^2+\frac{1}{a^2}$ for the conditions given below.

1. 14
2. 34
3. 27
4. 11

Q.

What is the coefficient of $x^3$ in (x-3)$(x+2{)}^2$ ?

1. 3

2. 1

3. 3

4. 4

Q.

Find the value of ${(\frac{1}{2a}+\frac{3}{4b})}^2$

1. $\frac{1}{4a^2}+\frac{9}{16b^2}+\frac{4}{3ab}$

2. $\frac{1}{4a^2}+\frac{9}{16b^2}+\frac{3}{4ab}$

3. $\frac{1}{16a^2}+\frac{9}{16b^2}+\frac{3}{4ab}$

4. $\frac{1}{4a^2}+\frac{3}{16b^2}+\frac{3}{4ab}$

Q.

What is the coefficient of $x^2$ in $(2x-4)(x+6{)}^2$ ?

1. 20

2. 9

3. 10

4. 11

Q.

State True or False

(−2x+5y−3z)² = 4x²+25y²+9z²−20xy−30yz+12zx

1. True
2. False

Q.

If $x\ne 0$ and $x+\frac{1}{2x}$ = 4, then find the value of $x^2+\frac{1}{4x^2}$

1. 20

2. 15

3. 10

4. 5

Q.

What is the coefficient of $x^3$ in (2x-4)$(x+6{)}^2$ ?

1. 2

2. 3

3. 4

4. 5

Q.

If $(x^2+\frac{1}{x^2}=7)$ , find $x-\frac{1}{x}$

1. $\pm$$\sqrt{(}5)$

2. 5

3. -5

4. $\pm$$\sqrt{(}7)$

Q. If $x+\frac{1}{x}=10$ and $x\ne 0$, then $x^2+\frac{1}{x^2}$ = ___.

1. 102
2. 98
3. 10
4. 100