Difference of Two Squares

Q.

Factorise:

$x^2-y^2-4xz+4z^2$

Q.

Factorise: $x^6-729$.

Q. a³ + b³ + a + b

Q. The factorisation of $a^4+b^4-7a^2{b}^2$ is equal to .

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

Q.

the factors of $a^2-1-2x-x^2$ are

1. (a - x + 1) (a - x - 1)

2. (a + x -1) (a - x + 1)

3. 
   (a +x +1) ( a- x - 1)

4. None of these

Q. Factorise:
(i) $4x^2+9y^2+16z^2+12xy-24yz-16xz$
(ii) $2x^2+y^z+8z^2-2\sqrt{2}xy+4\sqrt{2}yz-8xz$

Q. 8x³ +27y³ − 216z³ + 108xyz

Q. 8x²y³ − x⁵

Q.

The factors of $x^4+x^2+25$ are

1. $(x^2+3x+5)(x^2-3x+5)$
   
   

2. $(x^2+3x+5)(x^2+3x-5)$
   

3. $(x^2+x+5)(x^2-x+)$
   

4. None of these

Q. 125 + 8x³ − 27y³ + 90xy

Q.

Factorising and dividing $a^2+7a+10$ by (a + 5) gives:

1. a+1

2. 2

3. a+2

4. 1

Q.

One of the factors of $x^2-2x-15$ is:

1. x+3

2. x-3

3. x+5

4. x - 15

Q. Factorize each of the following expressions:

p³ + 27

Q. a¹²+ b¹²

Q. factorisation of $a^2+\frac{1}{a^2}-27$ is equal to .

1. $(a-\frac{1}{a}-5)(a-\frac{1}{a}+5)$
2. $(a-\frac{1}{a}-5)(a-\frac{1}{a}-5)$
3. $(a-\frac{1}{a}+5)(a-\frac{1}{a}+5)$
4. $(a+\frac{1}{a}-5)(a+\frac{1}{a}+5)$

Q. Factorise $x^2+\frac{1}{x^2}+2-5x-\frac{5}{x}$

1. $(x+\frac{1}{x})(x+\frac{1}{x}-5)$
2. $(x+\frac{1}{x})(x+\frac{1}{x}+5)$
3. $(x-\frac{1}{x})(x-\frac{1}{x}-5)$
4. $(x+\frac{1}{x})(x-5)$

Q.

Factorize : $x^2-1-2a-a^2.$

Q. Factorize:

64a³ + 125b³ + 240a²b + 300ab²

Q. x⁴y⁴ − xy

Q. The factors of 8a³ + b³ − 6ab + 1 are

(a) (2a + b − 1) (4a² + b² + 1 − 3ab − 2a)

(b) (2a − b + 1) (4a² + b² − 4ab + 1 − 2a + b)

(c) (2a + b + 1) (4a² + b² + 1 −2ab − b − 2a)

(d) (2a − 1 + b) (4a² + 1 − 4a − b − 2ab)

Q.

Factorise each of the following:

(i)

(ii)

[Hint: See question 9.]

Q.

Factorise: $27x^3+y^3+z^3-9xyz$

Q. 8x³ + 27y³ + 36x²y + 54xy²

Q. x³ − 12x(x − 4) − 64

Q. 64a³ − b³

Q.

Factorise:

(i)

(ii)

Q.

Factorise: $27x^3+y^3+z^3-9xyz$

Q.

Factorize:

$a^2-b^2+2bc-c^2$

Q. 27x³ − y³ − z³ − 9xyz

Q. Factorize each of the following expressions:

a³ + 8b³ + 64c³ − 24abc