Addition and Subtraction of Algebraic Expressions

Q. Prove that :

$\frac{a^{-1}}{(a{)}^{-1}+(b{)}^{-1}}+\frac{a^{-1}}{(a{)}^{-1}-(b{)}^{-1}}=\frac{2b^2}{b^2-a^2}$

Q.

Find the value of $A+B+C$ if :

$A=(7xy+5yz-3zx)$
$B=(4yz+9zx-4y)$
$C=(-3xz+5x-2xy)$

1. $5xy+3zx+5x-4y$

2. $5xy+9yz+3zx+4y$

3. $5xy+9yz+2zx+5x-4y$

4. $5xy+9yz+3zx+5x-4y$

Q.

$\Delta ABC$ is right angled at A. AB = 60 units, AC = 80 units and BC = 100 units. D is a point between B and C such that $\Delta ADB$ and $\Delta ADC$ have equal perimeters. What is the length of BD?

1. 10 units

2. 20 units

3. 60 units

4. 40 units

Q.

$\text{If two adjacent sides of a rectangle}\text{measure}(2x^2+y)m\text{and}(x^2-y)m,\text{then find its perimeter.}$

1. $6x^{2}m$

2. $-6x^{2}m$

3. $(6x^2-4y)m$

4. $(6x^2+4y)m$

Q. Question 3(ii)
Add the following:
(ii) a- b+ab, b - c +bc, c - a + ac

Q. Question 3(i)
Add the following:
(i) ab-bc, bc-ca, ca-ab

Q.

Question 41

State whether the following statement is true (T) or false (F).

In the equation 2x=4-x, transposing -x to LHS, we get x=4.

Q.

$4xy-10yx+26xy=$ ____.

1. $-20yx$

2. $20xy$

3. $10xy$

4. $-10yx$

Q. x ∝ $\frac{1}{\sqrt{y}}$ and when x = 40 then y = 16. If x = 10, find y.

Q. If the value of $p^2+q^2=21$ and $pq=30$, then find the value of $(p+q{)}^2$

1. 81

Q. Prove that :

$\frac{a^{-1}}{(a{)}^{-1}+(b{)}^{-1}}+\frac{a^{-1}}{(a{)}^{-1}-(b{)}^{-1}}=\frac{2b^2}{b^2-a^2}$

Q. Find constant of variation and write equation of variation for every example given below.
(1) p ∝ $\frac{1}{q}$ ; if p = 15 then q = 4
(2) z ∝ $\frac{1}{w}$ ; when z = 2.5 then w = 24
(3) s ∝ $\frac{1}{t^2}$ ; if s = 4 then t = 5
(4) x ∝ $\frac{1}{\sqrt{y}}$ ; if x = 15 then y = 9

Q. Solve the linear equation:

1. $m=\frac{7}{2}$
2. $m=\frac{3}{4}$
3. $m=\frac{7}{5}$
4. $m=\frac{4}{7}$

Q. Find the product of 5x, 6y and 7z

1. 180 xyz
2. 210 xyz
3. 240 x${}^2$yz
4. 150 xyz${}^2$

Q. Question 4
$\frac{3y+4}{2-6y}=\frac{-2}{5}$

Q. Simplify.
(1) (x − 2y +3)² + (x + 2y − 3)²
(2) (3k − 4r − 2m)² − (3k + 4r − 2m)²
(3) (7a − 6b + 5c)² + (7a + 6b − 5c)²

Q.

What must be added to $x^2+3x-8$ to get $x^2+x+6$?

1. 3 - 8

2. - 2x + 14

3. x + 6

4. 2x + 14

Q. must be subtracted from $4x^3-3x+5$ to get $2x^2-3x^3+5x-2$.

1. $x^3-2x^2-8x+7$
2. $7x^3+2x^2-8x+7$
3. $7x^3-2x^2-8x+3$
4. $7x^3-2x^2-8x+7$

Q.

Subtract $-3xfrom8x$.

Q.

If we subtract $-4x^{2}y$ from $2x^{2}y$, we get ______.

1. 6$x^2$$y^2$

2. $-6x{y}^2$

3. 6$x^{2}y$

4. -6$x^{2}y$

Q.

When $5a^{2}b+10b^2{c}^2-21ab+32$ is subtracted from $50-20b^2{c}^2-4bc-ac-5ab$, we get

1. $18+30b^2{c}^2-4bc-ac+16ab-5a^{2}b+10b^{2}c$

2. $18-30b^2{c}^2-4bc-ac+16ab-5a^{2}b$

3. $20-30b^2{c}^2-4bc-ac+16ab-5a^{2}b$

4. $22-30b^2{c}^2-4bc-ac-16ab-5a^{2}b$

Q. If the $a+\frac{4}{a}=4$, then what is the value of $a^4+\frac{1}{a^2}$?

1. 16.25

Q.

When $7xy+5yz-3zx$, $4yz+9zx-4y$ and $-3xz+5x-2xy$ are added, we get

1. 5xy + 9yz + 3zx - 5x – 4y

2. 5xy + 9yz + 3zx + 5x – 4y

3. 5xy + 9yz - 3zx + 5x – 4y

4. 5xy + 9yz + 15zx + 5x – 4y

Q. Find the third side of a triangle whose two sides are $(3x^2-5x)$ cm and $(4x^2+12)$ cm and perimeter is $(8x^2-9x+4)$ cm.

Q. $\frac{250}{50}$ and $\frac{x}{20}$ are directly proportional when x = .

1. 100
2. 50
3. 25

Q.

When $4yz+9zx-4y$ and $-3xz+5x-2xy$ are added, we get $4yz+6xz-2xy-4y+5x$.

1. False

2. True

Q.

An expression containing __________ unlike terms is called a binomial.

Q. The sum of $11x^2-8x+4$ and $6x^2+7x-10$ is

1. $17x^2+x-6$
2. $17x^2-x-6$
3. $17x^2-x+6$
4. $17x^2+x+6$

Q.

Which expression matches the statement "add 5x and 3x and then subtract the so obtained result from 12y”?

1. 5x + 3x - 12y

2. 5x + 3x + 12y

3. 12y - 5x + 3x

4. 12y - 5x - 3x

Q.

$ab+2ab$ is equal to

1. $2ab$

2. $-ab$

3. $3ab$

4. $ab$