Expansion of (a ± b)²

Q.

The value of $(102{)}^2+(98{)}^2$ is:

1. $20008$
2. $20068$
3. $20048$
4. $20018$

Q. The value of (101)${}^2$ - (99)${}^2$ is:

1. 39996
2. 33596
3. 32496
4. 36646

Q. The expansion of (2x-y)${}^2$ is:

1. 4x${}^2$ - 4xy + y${}^2$
2. 4x${}^2$ - 4xy + y${}^2$
3. 4x${}^2$ - 4xy + y${}^2$
4. 4x${}^2$ - 4xy + 64y${}^2$

Q.

If $({5x}^2+14x+2{)}^2$ – $({4x}^2-5x+7{)}^2$ is divided by $(x^2+x+1)$, then quotient q and remainder r are given by:

1. q = (+19x-5), r = 1

2. q = 9 (+19x-5), r = 0

3. q = (+19x-5), r = 0

4. q = 9 (+19x-5), r = 1

Q. The value of (99)${}^2$ is_____

1. 9901
2. 9801
3. 9981
4. 9991

Q. The value of (52)${}^2$ is:

1. 2704
2. 2684
3. 3704
4. 2564

Q.

When $5pq(p^2-q^2)$ is divided by $2p(p+q)$ and substituting $p=3$, $q=1$ the value obtained is _______ .

1. $5$

2. $2$

3. $6$

4. $8$

Q. The expansion of (x+2y)${}^2$ is:

1. 4x${}^2$ + 4xy + 4y${}^2$
2. x${}^2$ + 4xy + 4y${}^2$
3. x${}^2$ + 14xy + 4y${}^2$
4. x${}^2$ + 4xy + 16y${}^2$

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

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

Q. The value of (98)${}^2$ is______.

1. 9764
2. 9604
3. 9804
4. 9984

Q. The value of (105)${}^2$ is _______.

1. 11025
2. 11065
3. 12425
4. 11625

Q. State whether True or False.

1. True
2. False

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. The value of (105)${}^2$ + (95)${}^2$ is:

1. 39900
2. 41889
3. 34649
4. 40229

Q.

If $({5x}^2+14x+2{)}^2$ – $({4x}^2+14x+2{)}^2$ is divided by $(x^2+x+1)$, then quotient q and remainder r are given by -

1. q = (+19x-5), r = 0

2. q = 9 (+19x-5), r = 1

3. q = 9 (+19x-5), r = 0

4. q = (+19x-5), r = 1

Q. Which of the following is an identity?

1. $(t+3)(t-3)=t^2-9$
2. $(t+3)(t-3)=t^2+9$
3. $(t+3)(t-3)=t^2-9+3t$
4. none of these

Q. If the value of $a+\frac{1}{a}=3$, then the value of $a^4+\frac{1}{a^4}$ is equal to.

1. 45
2. 47
3. 49
4. 51

Q. The value of (107)${}^2$ - (93)${}^2$ is:

1. 20018
2. 10018
3. 36482
4. 23482

Q. If $a^2+\frac{1}{a^2}$ = 38, then the value of $a-\frac{1}{a}$ is equal to.

1. $\pm 4$
2. $\pm 5$
3. $\pm 6$
4. $\pm 7$