Applying Difference of Squares as a Product of Its Sum and Difference

Q.

Factorise the following expression: $a^4-2a^2{b}^2+b^4$

Q. Find the value of $97\times 103$ using a suitable algebraic identity.

1. 9991
2. 8999
3. 9999
4. 1111

Q. If $a+\frac{1}{a}=3$, then the value of $a^2+\frac{1}{a^2}$ is:_____.

1. 7
2. 9
3. 3
4. 27

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. $\pm 7$

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

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

Q.

Find the following product:$43\times 45$

1. 1935

2. 2115

3. 2025

4. 1835

Q.

Calculate the value of the expression using suitable identity $({23}^2-{22}^2{)}^2$

1. 2145

2. 2045

3. 2025

4. 2125

Q. Evaluate:
${\left(369\right)}^2–{\left(368\right)}^2$

1. 758
2. 737
3. 658
4. 637

Q. Find the value of ${22.9}^2-{7.1}^2$ using a suitable algebraic identity.

1. 574
2. 500
3. 474
4. 497

Q. Divide :
$15p^3÷3p$

Q.

Using identities, evaluate ${71}^2$

Q.

Compute the value of ${\left(6\frac{1}{2}\right)}^2-{\left(4\frac{1}{2}\right)}^2$

1. 22

2. 21

3. 24

4. 25

Q.

The value of the given expression $(284\times 116)-(246\times 154)$ is equal to $=4940$

1. False

2. True

Q.

Compute the value of ${34}^2-6^2$

1. - 3800

2. - 2200

3. - 3600

4. - 3200

Q.

Compute the value of ${8.2}^2-{1.8}^2$

1. 64

2. 64.2

3. 62.6

4. 62.4

Q. Divide: $81x^3(50x^2-98)$ by $27x^2(5x+7)$

Q.

Compute the following difference

$(228\times 172)-(234\times 66)$

1. $362$

2. $376$

3. $382$

4. $372$

Q.

The value of ${7.3}^2-{2.7}^2$ is equal to

1. $46$

2. $50$

3. $42$

4. $48$

Q.

Compute the following difference

$(11.6\times 10.4)-(11.3\times 10.7)$

1. $-0.54$

2. $-0.27$

3. $-0.81$

4. $-0.33$

Q.

The value of ${15.8}^2-{4.2}^2$ is equal to

1. $232$

2. $230$

3. $236$

4. $234$

Q.

Compute the value of ${2.7}^2-{1.3}^2$

1. 5.6

2. 5.8

3. 4.6

4. 5.2

Q.

Compute the value of ${9.2}^2-{0.8}^2$

1. $88$

2. $82$

3. $84$

4. $86$

Q. If $x+a$ is one of the factors of $p\left(x\right)=2x^2+2ax+5x+10$, then find $a$.

Q.

Compute the value of ${\left(4\frac{3}{4}\right)}^2-{\left(2\frac{1}{4}\right)}^2$

1. $14\frac{1}{2}$

2. $8\frac{3}{4}$

3. $28\frac{1}{2}$

4. $8\frac{1}{4}$

Q.

Evaluate: 103 × 104

1. 10, 712

2. 10, 812

3. 10, 512

4. 10, 612

Q. Use identities to evaluate: $(101{)}^2$

1. $11,601$
2. $12,761$
3. $10,111$
4. $10,201$

Q.

The value of 46^2 - 45^2 is equal to

1. 91

2. 92

3. 90

4. 89

Q.

The value of (8+5)^2 - (8-5)^2 is equal to

1. 150

2. 161

3. 151

4. 160

Q.

Find:
$(a+b+c)\times (a+b-c)=$

1. $a^2+4ab+b^2-c^2$

2. $a^2+2ab+b^2-c^2$

3. $a^2+2ab-c^2$

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

Q.

The value of 100^2 - 99^2 is equal to

1. 1

2. 99

3. 100

4. 199