Factors of a³ + b³

Q.

Divide $(m^2-14m-32)$ by $(m+2)$

Q. How many factors does the expression $x^9-x$ have?

Q. $\text{Divide}(-25x^{4}y)by5x^2.$

1. $-5xy$
2. $5x^{2}y$
3. $-5x^{2}y$
4. $-5x^2$

Q. Divide $49x^{2}y{z}^2$ by $7y^2{z}^3$ .

1. $\frac{7x}{yz}$
2. $\frac{7x^2}{yz}$
3. $\frac{7x^3}{yz}$
4. $\frac{7x^2}{y^{2}z}$

Q. Simplify the following expression:
$(5x-7y{)}^3+(5x+7y{)}^3$
(4 Marks)

Q.

Question 72

In the following question, state whether the statement is True (T) or False (F):

Common factor of $12a^2{b}^2+4a{b}^2-32$ is 4.

Q. Which of the following represents the prime factorization of 24?

1. $2\times 2\times 2\times 3$
2. $3\times 8$
3. $2\times 2\times 6$
4. $4\times 6$

Q. $\frac{27x^{3}y}{9x^2}=$ ______.

1. $9x^{2}y$
2. $9x{y}^2$
3. $9xy$
4. $3xy$

Q. One of the factors of $x^2+\frac{1}{x^2}+2-2x-\frac{2}{x}$ is:

1. $x-\frac{1}{x}$
2. $x-\frac{1}{x}-1$
3. $x+\frac{1}{x}$
4. $x^2+\frac{1}{x^2}$

Q.

$(a+b{)}^3-(a-b{)}^3$ =________

1. $b^3+3a^{2}b$

2. $2(b^3+3a^{2}b)$

3. 0

4. $2(a^3+3a{b}^2)$

Q. What are the factors of $15xyz$?

1. 3
2. 5
3. 6
4. x+1
5. xy
6. xyz
7. 1
8. 2
9. x + y + z
10. x

Q. Factorisation of $-x^{2}y-x+3xy+3$ gives _________ .

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

Q. Factors for $a^2{b}^2+c^2{d}^2-a^2{c}^2-b^2{d}^2$ are:

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

Q. $\text{Factorise:}12xy-8x+9y-6$

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

Q.

Which of the following is the factorised form of $20l^{2}m+30alm?$

1. $10lm(2l+3a)$
2. $10lm(2l-3a)$
3. $5lm(2l+3a)$
4. $10lm(l+3a)$

Q. $Divide\left(24x{y}^2{z}^3\right)by\left(6y{z}^2\right).$

1. $4x{y}^{2}z$
2. $4x{y}^2{z}^2$
3. $4xyz$
4. $4x{y}^2$