Algebraic Identities

Q.

Solve the following equation by factorisation:

√3 x ²+10x+7√3=0

Q.

How to factorise

3x² - 3√2x + 1.

Q.

Question 26
Factorise the following:
(i) $4x^2+20x+25$

(ii) $9y^2–66yz+121z^2$

(iii) ${(2x+\frac{1}{3})}^2-{(x-\frac{1}{2})}^2$

Q. If a and b are unequal and X^2+ ax + b and x^2+ bx + a have a common factor then the value of a + b is

Q.

If x+y=-2, then $x^3$+$y^3$+8 equals

1. (x+y+2)³

2. 6xy

3. -6xy

4. zero

Q. 4. X square - X - 1 , value of X by middle term split

Q.

If a + b + c = 2s, then prove the following identities

(a) s² + (s − a)² + (s − b)² + (s − c)² = a² + b² + c²

(b) a² + b² − c² + 2ab = 4s (s − c)

(c) c² + a² − b² + 2ca = 4s (s − b)

(d) a² − b² − c² + 2ab = 4(s − b) (s − c)

(e) (2bc + a² − b² − c²) (2bc − a² + b² + c²) = 16s (s − a) (s − b) (s − c)

(f)

Q. 4x²+4x+1

Q. should be added to ${4x}^2-4x$ to make it a perfect square.

1. 1
2. -1
3. 0

Q.

Factorise: abx + aby - bcx - bcy

Q. Consider the set $A=3,4,5$ and the numbers of null relations, identity relation, universal relations, reflexive relations on $A$ are respectively $n_1,n_2,n_3$ and $n_4$ then the value of $n_1+n_2+n_3+n_4$ is equal to

1. $8$
2. $7$
3. $73$
4. $67$

Q. What is Expansion of $(x-y{)}^3$?

1. $x^3-y^3+3xy(x-y)$
2. $x^3+y^3-3xy(x+y)$
3. $x^3-y^3-3xy(x-y)$
4. $x^3+y^3+3xy(x+y)$

Q. how to factorize x3-6x2+11x-6

Q.

What is the value of $e^{ln{x}^2}$?

1. $x$

2. $x^2$

3. $2x$

4. Not possible to simplify

Q.

Check whether $4^n$ can end with the digit 0 for any natural number n.

Q.

Using a suitable identity, the value of (1 – cos²A) cosec²A is

1. 1

2. 2

3. -1

4. 0

Q.

Using Euclid’s division algorithm, find the HCF of 20 and 55.

Q.

Express the following sets in set-builder form.
1. {1, 4, 9, ……..81}
2. {1, 5, 25, 125, 625, 3125}
3. {3, 6, 9, 12, 15, 18}

Q.

Write the following cubes in expanded form:
$\left(i\right)(2x+1{)}^3$
$\left(ii\right)(2a-3b{)}^3$
$\left(iii\right){[\frac{3}{2}x+1]}^3$
$\left(iv\right){[x-\frac{2}{3}y]}^3$

Q.

Using factor theorem factorise the expression completely: 3³ + 2² – 19 + 6

1. (x – 2)(3x – 1)(x + 3)

2. (x – 2)(3x + 1)(x + 2)

3. (x – 2)(3x - 1)(x + 2)

4. (x + 2)(3x + 1)(x – 1)

5. (x + 2)(3x – 1)(x – 2)

6. (x + 2)(3x – 1)(x + 3)

Q.

Express the following sets in set-builder form.
1. {1, 4, 9, ……..81}
2. {1, 5, 25, 125, 625, 3125}
3. {3, 6, 9, 12, 15, 18}

Q.

Solve by factorisation (quadratic equations)

1/2a+b+2x = 1/2a+ 1/b +1/2x

Q.

factorise completely

2x + 4y + px + 2py

please explain this problem elaborately becaue i have my board exam tomorrow and i need help as fast as possible

Q. If is added to $x^2+8x$, it will become a perfect square.

1. 16
2. -16
3. 0

Q. By what number should 85 be divided to get 16 as quotient and 5 as remainder?

1. 10
2. 6
3. 8
4. 5

Q. Find the largest number that will divide 398, 436 and 542 leaving remainders 7, 11 and 15 respectively.

1. 527
2. 13
3. 17
4. 491

Q. 17. Factorise it: 1/(2x-3) + 1/(x-5)=10/9

Q. FIND THE ROOTS OF THE FOLLOWING QUADRATUC EQUATION BY FACTORISATION (i) 2x^2-x+1/8=0 (ii) \sqrt{2x^{ 2 }}+ 7x +\sqrt[5]2=

Q. The expression $a^3+b^3+c^3-3abc$ can be expressed as a product of two expressions. What is the product?

1. $(a+b+c)\times (a^2-b^2-c^2-ab-bc-ca)$
2. $(a-b-c)\times (a^2+b^2+c^2-ab-bc-ca)$
3. $(a+b+c)\times (a^2+b^2+c^2+ab+bc+ca)$
4. $(a+b+c)\times (a^2+b^2+c^2-ab-bc-ca)$

Q. factorize: 35x² + 4xy - 4y² + 12yz - 6xz - 9z²