Algebraic Quadratic Identity

Q. Calculate $103\times 107$ using algebraic identities.

1. 10121
2. 11021
3. 10021
4. 12011

Q. $\text{If}(a+\frac{1}{a})=5,$
$\text{then find the value of}(a^2+\frac{1}{a^2}).$

1. 45
2. 25
3. 23
4. 32

Q. What is the expansion for the identity ${(a–b)}^2$?

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

Q. Question 5(iv)
Show that:
$(4pq+3q{)}^2-(4pq-3q{)}^2=48p{q}^2$

Q.

Question 85 (x)

Expand the following, using suitable identities.

$(2x-5y)(2x-5y)$

Q. $\text{Factorise}:m^4-256$.

1. $(m-4)(m+4)(m^2+4)$
2. $(m-8)(m+8)(m^2+16)$
3. $(m-4)(m+4)(m^2+8)$
4. $(m-4)(m+4)(m^2+16)$

Q.

Evaluate ${(x+4)}^2$

Q. Find the value of :
$\left(i\right)\frac{6.25\times 6.25-1.75\times 1.75}{4.5}\left(ii\right)\frac{198\times 198-102\times 102}{96}$
Choose the correct answers from the given options .

1. 8
2. 100
3. 300
4. 10

Q. Question 1(viii)
Use a suitable identity to get each of the following products:
$(-a+c)(-a+c)$

Q.

Question 85 (vii)

Expand the following, using suitable identities.

$(2x+9)(2x-7)$

Q.

Question 85 (ii)

Expand the following, using suitable identities.

$(x^{2}y-x{y}^2{)}^2$

Q. If $x+\frac{1}{x}=20$, then the value of
$x^2+\frac{1}{x^2}$ is .

1. 402
2. 398
3. 395
4. 405

Q. The value of $(7xy+3x{)}^2-(7xy-3x{)}^2$ is ____________.

1. $84x^{2}y$
2. $98x^2{y}^2+18x^2+76x^{2}y$
3. $49x^2{y}^2+18x^2+84x^{2}y$
4. $42x^{2}y$

Q. If $x-\frac{1}{x}=7,$ then find the value of
$x^2+\frac{1}{x^2}.$

1. 49
2. 51
3. 53
4. 47

Q.

The value of $(1{)}^{-2}$ + ${\left(\frac{1}{2}\right)}^{-2}$ +${\left(\frac{1}{3}\right)}^{-2}$+ ${\left(\frac{1}{4}\right)}^{-2}$ is 30.

1. False

2. True

Q. Using a suitable identity, we can find out that $(2y+5)(2y+5)$ is equal to

1. $4y^2+10y+25$
2. $4y^2+20y+25$
3. $4y^2+20y+15$

Q. (${98}^2$) = . (Evaluate using identities.)

1. 9804
2. 9604
3. 9984
4. 9544

Q.

Question 1(i)

Use a suitable identity to get each of the following products:
$(x+3)(x+3)$

Q.

Question 85 (xv)

Expand the following, using suitable identities.

$(0.9p-0.5q{)}^2$

Q. $(2y+5)(2y+5)$ =

1. $4y^2+10y+25$
2. $4y^2+20y+25$
3. $4y^2+20y+15$
4. $y^2+20y+25$

Q. Show that:
$(9p-5q{)}^2+180pq=(9p+5q{)}^2$

Q. Using identities, evaluate 95 $\times$ 105.

1. 9999
2. 9975
3. 9950
4. 9925

Q. (${107}^2$) = . (Evaluate using identities.)

1. 11449
2. 11249
3. 16269
4. 18149

Q.

Using suitable algebraic identity, find the value of ${\left(4.9\right)}^2$.

1. 24.01
2. 25
3. 24.25
4. 24

Q.

The value of $(109{)}^2$ is _______.

1. 11881

2. 10881

3. 11880

4. 11891

Q. Use a suitable identity to get each of the following products:
(1.1m – 0.4 ) (1.1m + 0.4 ).

Q. If $x+\frac{1}{x}=20$, then the value of
$x^2+\frac{1}{x^2}$ is _____.

1. 395
2. 405
3. 402
4. 398

Q. One of the factors of the expression 𝑚^2 + 7𝑚 + 12 can be:

1. m + 5
2. m + 4
3. m - 3
4. m - 4

Q.

$(x+y)(x-y)(x^2+y^2)$ = ___________.

1. $x^3-y^3$

2. $x^3+y^3$

3. $x^4+y^4$

4. $x^4-y^4$

Q. The value of ${31}^2$ =

1. 961
2. 963
3. 900