Algebraic Identities

Q.

What is the formula of $a^2+b^2+c^2$ $?$

Q.

If $(x-\frac{1}{x})=6$, then $(x^2+\frac{1}{x^2})=?$

(a) $36$
(b) $38$
(c) $32$
(d) $36\frac{1}{36}$

Q.

Which of the following is correct?
a) $(a-b{)}^2=a^2+2ab-b^2$
b) $(a-b{)}^2=a^2-2ab+b^2$
c) $(a-b{)}^2=a^2-b^2$
d) $(a+b{)}^2=a^2+2ab-b^2$

Q.

If $(a-b)=7$ and $ab=9$ then $(a^2+b^2)=?$
(a) 67
(b) 31
(c) 40
(d) 58

Q.

$If{x}^2+\frac{1}{x^2}=18,\text{find the values of}x+\frac{1}{x}andx-\frac{1}{x}.$

Q.

$Ifx+y=4andxy=2,\text{find the value of}{x}^2+y^2.$

Q.

$Ifx+\frac{1}{x}=12,\text{find the value of}x-\frac{1}{x}.$

Q.

Factorize the expression $x^6-7x^3-8$.

Q.

Question 4(v)
Simplify:
$(2.5p-1.5q{)}^2-(1.5p-2.5q{)}^2$

Q.

Factorise $\left(x^2-2xy+y^2\right)-z^2$

Q.

A ___ of shoes (Fill in the blanks with collective noun )

1. swarm

2. bunch

3. pair

4. none of the above

Q.

$Ifx+\frac{1}{x}=9,\text{find the value of}{x}^4+\frac{1}{x^4}.$

Q.

A ___Of Girls. Fill In The Blanks With A Collective Noun.

Q.

$\cos \left[{\tan }^{-1}\left(\frac{1}{3}\right)+{\tan }^{-1}\left(\frac{1}{2}\right)\right]=?$

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

2. $\frac{\sqrt{3}}{2}$

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

4. $\frac{\mathrm{\pi }}{4}$

Q.

If $x-y=7$ and $xy=9$, find the value of $(x^2+y^2)$

Q.

Using suitable identities, evaluate the following:

$98\times 103$

Q.

Find the value of each of the following using the short-cut method:
1.$(25{)}^3$ 2. $(47{)}^3$ 3. $(68{)}^3$ 4. $(84{)}^3$

Q.

Factorize $4x^2+y^2+z^2-4xy-2yz+4xz$

Q. Using an identity, evaluate
$297\times 303.$

1. 90001
2. 89998
3. 89991
4. 90008

Q.

$Ifx+\frac{1}{x}=20,\text{find the value of}{x}^2+\frac{1}{x^2}.$

Q. Factorise:2x^2+5x-1

Q.

Using identities. Evaluate

1.05X9.5

Q. The sum of two rational number is 3/2. If one of them is -3/10, find the other.

Q. Simplify the following expression:
$(ab+bc)(ab-bc)+(bc+ca)(bc-ac)+(ca+ab)(ac-ab)$

1. -2
2. 0
3. $2\left[\right(ab{)}^2+(bc{)}^2+(ac{)}^2]$
4. 2

Q. Question 8(i)
Using $(x+a)(x+b)=x^2+(a+b)x+ab$, find
$103\times 104$

Q. Verify that $(x÷$y)^{-1} =$x^{-1}÷y^{-1}$, if $x=\frac{-15}{26},y=\frac{5}{13}$ [4 MARKS]

Q.

Question 86 (x)

Using suitable identities, evaluate the following:

$104\times 97$

Q.

$If3x+5y=11andxy=2,\text{find the value of}9x^2+25y^2$

Q.

Find the value of the expression
$(9x^2+24x+16)$ when $x=12$

Q.

Add the following:$2p^2{q}^2-3pq+4,5+7pq-3p^2{q}^2$