# Free Algebraic Expressions and Identities 01 Practice Test - 8th Grade

When 7xy+5yz3zx, 4yz+9zx4y and 3xz+5x2xy are added, we get ___.

A.

5xy+9yz+3zx+5x4y

B.

5xy+9yz+15zx+5x4y

C.

5xy+9yz3zx+5x4y

D.

5xy+9yz+3zx5x4y

#### SOLUTION

Solution : A

7xy+5yz3zx
4yz+9zx4y
2xy           3xz          +5x________________________
5xy+9yz+3zx4y+5x

What must be subtracted from (4x33x+5) to get (2x23x3+5x2) ?

A.

x32x28x+7

B.

7x3+2x28x+7

C.

7x32x28x+3

D.

7x32x28x+7

#### SOLUTION

Solution : D

4x33x+5
3x3+5x2+2x2

(+)   ()   (+)   ()
________________________
7x38x+72x2

=7x32x28x+7

Add (3+2y5y2+6y3),   (8+3y+7y3) and (56y8y3+y2).

A.

3y4y2+5y3

B.

y3y2+5y3

C.

y4y2+5y3

D.

y4y2+6y3

#### SOLUTION

Solution : C

To add :  (3+2y5y2+6y3), (8+3y+7y3) and (56y8y3+y2)

(8+3y+7y3) does not have the term with y2. So, we add 0y2 and hence, the expression will be (8+3y+0y2+7y3).

On adding there expressions, we get,
3+2y5y2+6y3
8+3y+0y2+7y3
56y+y2 8y3––––––––––––––––––––
1y4y2+5y3

(3+2y5y2+6y3)+(8+3y+7y3)+(56y8y3+y2)=(y4y2+5y3)

(1.05)2(0.95)2= ___

#### SOLUTION

Solution :

Using the identity
(a)2(b)2=(a+b)(ab) ,
(1.05)2(0.95)2
=(1.05+0.95)(1.050.95)
=(2)(0.1)=0.2

(4pq+3q)2  (4pq3q)2= ____________.

A.

44pq2

B.

48p2q

C.

48pq2

D.

44p2q

#### SOLUTION

Solution : C

(4pq+3q)2(4pq3q)2

We have:

(a+b)2=a2+2ab+b2(ab)2=a22ab+b2

So, (4pq+3q)2(4pq3q)2

=[(4pq)2+(3q)2+2(4pq)(3q)][(4pq)2+(3q)22(4pq)(3q)]

=24pq2+24pq2
=48pq2

Using an identity expand :
(2y+5)(2y+5)

A.

4y2+10y+25

B.

4y2+20y+25

C.

4y2+20y+15

D.

y2+20y+25

#### SOLUTION

Solution : B

We know that,
(a+b)×(a+b)=(a+b)2

Using the identity
(a+b)2=a2+2ab+b2,

(2y+5)(2y+5)=(2y+5)2
=(2y)2+2(2y)(5)+52
=4y2+20y+25

A monomial multiplied by a monomial always gives a ________.

A.

Monomial

B.

Binomial

C.

Trinomial

D.

Constant

#### SOLUTION

Solution : A

When we multiply monomials, we first multiply the coefficients and then multiply the variables by adding the exponents. This will always give a monomial.

For example, 2ab×2b= 4ab2, which is a monomial.

The numerical factor of a term is known as

A.

Expression

B.

Coefficient

C.

Variable

D.

Equation

#### SOLUTION

Solution : B

The numerical factor of a term is known as coefficient.

Simplify (3x2+5y2)(4xy5y).

A.

(6x3y15xy+20xy35y3)

B.

(12x3y5x2y+10xy3+25y3)

C. (12x3y15x2y+20xy325y3)
D. (6x3y15x2y+10xy35y3)

#### SOLUTION

Solution : C

Given: (3x2+5y2)(4xy5y)
=3x2(4xy5y)+5y2(4xy5y)
=12x3y15x2y+20xy325y3

Find the area of a rectangle whose length is 5xy units and breadth is 8xy2 units.

A.

40x2y3 square units

B.

40x2y2 square units

C.

40xy3 square units

D.

40xy square units

#### SOLUTION

Solution : A

Given:
Length of the rectangle = 5xy units
Breadth of the rectangle = 8xy2 units

Area of the rectangle = length × breadth
=5xy×8xy2
=40x2y3 square units

Hence, the area of the rectangle is 40x2y3 square units.