Simplification of Rational Algebraic Expression

Q. ($p^3{q}^6-p^6{q}^3)÷p^3{q}^3$ = _________.

1. $p^3-q^3$
2. $p^3+q^3$
3. $q^3-p^3$
4. $-p^3-q^3$

Q. The factors of $x^3-64$ are ______________.

1. $(x-3)and(x^2+3x+9)$
2. $(x-4)(x^2+4x+16)$
3. $(x+3)and(x^2+4x+16)$
4. $(x+4)and(x^2-4x-16)$

Q.

The quotient of $x$ and $y$, if $x$ is divided by $y$, added to the product of $x$ and $y$

Q.

Work out the following division: $96abc(3a-12)(5b-30)÷144(a-4)(b-6)$

Q. The simplified form of $\frac{x^2-9y^2}{x^3-27y^3}$ is _______.

1. $\frac{x+3y}{x^2+3xy+9y^2}$
2. $\frac{x^2+3xy+9y^2}{x+3y}$
3. $\frac{x^2+6xy+9y^2}{x+3y}$
4. $x+3y$

Q. Factorise the trinomial $x^2-x-12$.

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

Q. Resolve the following quadratic trinomial into factors:

$(x-2y{)}^2-5(x-2y)+6$

Q.

Question 84 (iv)

Simplify

${(\frac{3}{4}x-\frac{4}{3}y)}^2+2xy$

Q. Question 4(ii)
Divide as directed
$26xy(x+5)(y-4)÷13x(y-4)$

Q.

Question 4(iii)
Divide as directed
$52pqr(p+q)(q+r)(r+p)÷104pq(q+r)(r+p)$

Q.

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

Q.

The sum of the factors of $78$ is

Q. $10y(6y+21)÷5(2y+7)$ = _________.

1. $10y$
2. $6y$
3. $(2y+7)$
4. $(6y+21)$

Q. $(p^3{q}^6-p^6{q}^3)÷p^3{q}^3=$______

1. $q^3-p^3$
2. $q^3+p^3$
3. $p^3-q^3$
4. $p^3+q^3$

Q. $(x^3+2x^2+3x)÷2x$ = ___________.

1. $x^2+2x+3$
2. $2x^2+2x+3$
3. $2x^2+2x+6$
4. $\frac{1}{2}(x^2+2x+3)$

Q. The degree of the quotient when $6x^3+3x$ is divided by 3x is ___

Q.

Number $56$ has $6$ factors.

1. True
2. False

Q.

The value of $\frac{x(x+1)(x+2)(x+3)}{x(x+1)}$ is __________.

1. (x+3)

2. x(x+1)

3. (x + 2) (x + 3)

4. (x+2)

Q. Factorise the expressions and divide them as directed.
$(y^2+7y+10)÷(y+5)$
[3 marks]

Q. Question 3(iii)
Work out the following divisions
$10y(6y+21)÷5(2y+7)$

Q.

Akash has $6xy+4x{y}^2$ chocolates. He wants to distribute them to 2x children. How many chocolates does each of the child get if y = 2?

___

Q.

On dividing $\left(24x{y}^2\right)\left(z^2\right)$ by $6y{z}^2$, we get

1. 4xy

2. 4yz

3. 4xyz

4. 4xz

Q.

Which of the following is the expression obtained by the division of $5pq(p^2-q^2)$ by $2p(p+q)?$

1. $\frac{5q(p-q)}{2}$

2. $\frac{5q(p+q)}{4}$

3. $\frac{5q(p-q)}{4}$

4. $\frac{5q(p+q)}{2}$

Q.

Find the value of the given expression
$(x^3+2x^2+3x)÷2x$

1. 1/2(x²+2x+3)

2. 1/2

3. (x²+2x+3)

4. 1

Q.

State whether true or false:
$\frac{(3x^2+1)}{\left(3x^2\right)}=1+1=2$

1. True

2. False