Free Algebraic Expressions and Identities 02 Practice Test - 8th Grade

What must be subtracted from (x33x2+5x1) to get (2x3+x24x+2) ?

A.

x3+4x2+9x3

B.

x34x2+6x3

C.

x34x2+9x9

D.

x34x2+9x3

SOLUTION

Solution : D

Let the expression to be subtracted be y.

Hence,
(x33x2+5x1)y=2x3+x24x+2

On rearranging the terms,
y=(x33x2+5x1)(2x3+x24x+2)

y=x33x2+5x12x3x2+4x2

y=x32x33x2x2+5x+4x12

y=x34x2+9x3

So we have to subtarct (x34x2+9x3) to get the required value.

Subtract 7x3x2 from 4x+8x2

A.

3x

B.

11x25x

C.

11x2

D.

11x23x

SOLUTION

Solution : D

4x+8x2
7x3x2
()   (+)
____________
3x+11x2

Find the sum of
(11x28x+4) and (6x2+7x10).

A.

17x2x6

B.

17x2x+6

C.

17x2+x6

D.

18x2x6

SOLUTION

Solution : A

To find : Sum of (11x28x+4) and (6x2+7x10)

On adding the like terms together, we get,

11x28x+4
+  6x2+7x10––––––––––––––––
17x2x6

Find the value of 362352=

___

SOLUTION

Solution :

Using the Identity (x+a)(xa)=x2a2

We Put x = 36 and a = 35

(36 + 35) (36 - 35) = (71) (1) = 71

Simplify:
(xy+yz)2(xyyz)2

A.

4xy2

B.

4xy2z

C.

4xz

D.

4xy2z

SOLUTION

Solution : B

Using the identity,
(a+b)2=a2+b2+2ab,

we get,
(xy+yz)2=x2y2+y2z2+2xzy2...(1)

Using the identity,
(ab)2=a2+b22ab

we get,
(xyyz)2=x2y2+y2z22xzy2...(2)

Subtracting (2) from (1), we get

(x2y2+y2z2+2xzy2)(x2y2+y2z2 2xzy2)
=2xzy2+2xzy2
=4xy2z

Simplify (xy+yz)22x2y2z and find it's value when x=1,y=1 and z=2

A.

3

B.

4

C.

-3

D.

0

SOLUTION

Solution : C

(xy+yz)2 is in the form of (a+b)2 where a=xy and b=yz.
Using (a+b)2=a2+b2+2ab,
(xy+yz)2=x2y2+y2z2+2xzy2.

Therefore,
(xy+yz)22x2y2z=x2y2+y2z2+2xzy22x2y2z

Substituting the values of x,y and z in the above expression, we get
x2y2+y2z2+2xzy22x2y2z
(1)2(1)2+(1)2(2)2+2(1)(2)(1)22(1)2(1)2(2)
1 + 4 - 4 - 4 = -3

Which of the following is an algebraic expression?

A.

x23

B.

4x + 7

C.

3

D.

x = 10

SOLUTION

Solution : A, B, and C

An algebraic expression consists of variables, constants and operators (+, -, / ,x). An algebraic expression is the sum of algebraic terms.

When an algebraic expression is equated to another algebraic expression or zero, it becomes an algebraic equation.

• x23 has the variable x, constant term 3 and the operator .
• 4x+7 has the variable x, constant term 7 and the operator +.
• 3 can be written as 3x0+0 which has a variable term, constant term and the operator.

Hence, x23,4x+7 and 3 are algebraic expressions where as x=10 is an algebraic equation.

Which of the following is a binomial?

A.

2x + 7

B.

4x + y + 2

C.

7 - 3x + 4y

D.

3x

SOLUTION

Solution : A

A polynomial which involves two terms is called a binomial. For example, 3y + 9, 4a - 10 etc.

(a+b+c)(a+b-c) = ___________.

A.

a2+2abc2

B.

a2+4ab+b2c2

C.

a2+2ab+b2

D.

a2+2ab+b2c2

SOLUTION

Solution : D

(a+b+c)(a+bc)=
(a2+abac+ab+b2bc+ac+bcc2)
=(a2+2ab+b2c2)

5x×(4yz)×3xz = ___

A.

60xyz

B.

15x2z24yz

C.

60xyz

D.

60x2yz2

SOLUTION

Solution : D

On multiplying x with x, its power is raised to 2 i.e.,  x×x=x2
On multiplying z with z its power is also raised to 2 .
i.e.,
z×z=z2
Multiply all the coefficients to get 5×(4)×3=60

Therefore, the answer is 60x2yz2.