Rational Algebraic Expression

Q.

Factorise the expression and divide them as directed: $\left(5p^2-25p+20\right)÷\left(p-1\right)$.

Q. Factors of $a^2-a+ab-b$ are __________.

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

Q. Simplify :$\frac{9x^2-y^2}{3x^2-10xy+3y^2}$

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

Q.

Dividing $4x^2-10x+6$ by $2$, we get ______.

1. $4x^2-10x+6$

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

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

4. $4x^2+10x-6$

Q.

Dividing $4x^2-10x+6$ by $2$, we get ______.

1. $4x^2-10x+6$

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

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

4. $4x^2+10x-6$

Q. Find the expansion of the following:
$(6-4a-7b{)}^2$

Q. a^3 - b^3 = ______.

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

Q. If A and B are two algebraic expressions, then A/B is called a/an ____________ algebraic expression.

1. irrational
2. rational
3. improper
4. proper

Q. If A and B are two algebraic expressions, then A/B is called a/an ____________ algebraic expression.

1. irrational
2. rational
3. improper
4. proper

Q. ___________ is a factor of the algebraic expression 4xy+8x(y)^2.

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

Q. is a factor of $4xy+2y+6x+3$.

1. $(2x+3)(2y+3)$
2. $(2x+1)(y+3)$
3. $(2x+1)(2y+6)$
4. $(2x+1)(2y+3)$

Q. The factors of $p^2+6p-16$ are __________.

1. (p-2)(p+8)
2. (p+2)(p-8)
3. (p+2)(p+8)
4. (p-2)(p-8)

Q. The value of $(2x+3y{)}^3-(2x-3y{)}^3$ is _____.

1. $72x^{2}y+54y^3$
2. $54x^{2}y+72y^3$
3. $72x^{2}y$
4. $54x^{2}y$

Q. Expansion of (a + b)${}^3$ is

1. a${}^3$ + 3a${}^2$b - 3ab${}^2$ + b${}^3$
2. a${}^3$ - 3a${}^2$b - 3ab${}^2$ + b${}^3$
3. a${}^3$ + 3a${}^2$b +3ab${}^2$ + b${}^3$
4. None of these

Q. Which of the following is the common factor of 4ab, 6bc and 8abc?

1. 3a
2. 4b
3. 2b
4. 2c