Expansion of (x+y)^2

Q.

If $a+\frac{1}{a}=3;find=a^2+\frac{1}{a^2}$

Q.

How to do factorization with algebraic identities ? Give each examples from every identities

Q.

Expand the following, using suitable identities: ${(3a-7b-c)}^2$

Q. $\text{Multiply}{x}^2+2y\text{by}{x}^3–2xy+y^3\text{and find the value of the product for}x=1\text{and}y=-1.$

Q.

Using identities, evaluate:
$10.5\times 9.5$.

1. 9975

2. 9.975

3. 99.75

4. 0.9975

Q. 25-a^2-b^2-2ab

Q.

Expand the following using identities $(3x-4y{)}^2$.

Q.

If $m-\frac{1}{m}=5,$ find :

(i) $m^2+\frac{1}{m^2}$

(ii) $m^4+\frac{1}{m^4}$

(iii) $m^2-\frac{1}{m^2}$

Q.

If $a^2+\frac{1}{a^2}=23;finda+\frac{1}{a}$

Q.

If $a+\frac{1}{a}=2$ , find $\frac{a^4+1}{a^2}$

1. 4

2. 2

3. 8

4. 16

Q.

If $a^2+b^2=41andab=4,$ find :

(i) (a - b)

(ii) (a + b)

Q.

If 4x² + y² = 40 and xy = 6, find 2x + y.

Q. (4/11)^x-1 = (11/4)^x-5. Find the value of x.

Q.

If $2a+\frac{1}{2a}=8$, find :

(i) $4a^2+\frac{1}{4a^2}$

(ii) $16a^4+\frac{1}{16a^4}$

Q.

If $a+\frac{1}{a}=2,$ Find :

(i) $a^2+\frac{1}{a^2}$

(ii) $a^4+\frac{1}{a^4}$

Q.

49(a-b)^2 -25(a+b)^2 factorize?

Q.

If $a^2+b^2=29andab=10$; find :

(i) a + b (ii) a - b

Q.

A side of a square was increased 4 times. What was the change in Area?

1. 20 times

2. Two times

3. 16 times

4. 4 times

Q.

x^2+4abx-(a^2-b^2)^2

Q.

$a^2+\frac{1}{a^2}=2$ then $\frac{1}{a}+a$=?

Q. Using identities, evaluate:
${71}^2$

1. 5401
2. 4911
3. 4941
4. 5041

Q. 44. the unique value of x satisfying the equation 4^x-3^(x-(1/2))=3^(x+(1/2))-2^(2x-1) is equal to

Q.

Using identities, evaluate:
${8.9}^2$

1. $80.21$

2. $64.81$

3. $79.21$

4. $79.31$

Q.

Evaluate :

Using expansion of $(a+b{)}^{2}or(a-b{)}^2$

(i) $(208{)}^2$

(ii) $(92{)}^2$

(iii) $(415{)}^2$

(iv) $(188{)}^2$

(v) $(9.4{)}^2$

(vi) $(20.7{)}^2$

Q.

Find the square of :

(i) $x+3y$

(ii) $2x-5y$

(iii) $a+\frac{1}{5a}$

(iv) $2a-\frac{1}{a}$

(v) $x-2y+1$

(vi) $3a-2b-5c$

(vii) $2x+\frac{1}{x}+1$

(viii) $5-x+\frac{2}{x}$

(ix) $2x-3y+z$

(x) $x+\frac{1}{x}-1$

Q. ${101}^2$ = (using identities)

1. 10, 209
2. 10, 201
3. 10, 401
4. 10, 211

Q.

Find the square of :

(i) $3x+\frac{2}{y}$

(ii) $\frac{5a}{6b}-\frac{6b}{5a}$

(iii) $2m^2-\frac{2}{3}{n}^2$

(iv) $5x+\frac{1}{5x}$

(v) $8x+\frac{3}{2}y$

(vi) $607$

(vii) $391$

(viii) $9.7$

Q.

If $a^2+b^2=14$ and $ab=3$, find the value of $2(a+b{)}^2-5(a-b{)}^2$.

1. 16

2. 0

3. 20

4. 32

Q. Simplify:
(i) $(a^2-b^2{)}^2$
(ii) $(2x+5{)}^2-(2x-5{)}^2$
(iii) $(7m-8n{)}^2+(7m+8n{)}^2$
(iv) $(4m+5n{)}^2+(4n+5m{)}^2$

Q. If 10^2y=25 then what is the value of 10^y