# Free Algebraic Expressions and Identities 03 Practice Test - 8th Grade

When we add 5a2b+6ab+7bc+54 and 14ab+8bc+16, we get:

A.

5a2b+20ab+7bc+70

B.

5a2b+6ab+7bc+8ac+70

C.

5a2b+16ab+7bc+8ac+70

D.

5a2b+20ab+15bc+70

#### SOLUTION

Solution : D

5a2b+6ab+7bc+54
14ab+8bc+16
________________________________
5a2b+20ab+15bc+70

Subtract( 86x+x27x3+x5) from( x46x3+x23x+1).

A.

x5+x4+x3+3x

B.

x5+x4+x37

C.

x5+x4+x3+3x7

D.

x5+x4+4x3+3x7

#### SOLUTION

Solution : C

x46x3+x23x+1   x57x3+x26x+8()(+)()(+)()x5+x4+x3+3x7

=(x5+x4+x3+3x7)

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 unknown be =y

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

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

x33x2+5x1
2x3+ x24x+2
()  ()    (+)   ()
____________________
x34x2+9x3

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

997×998= ___

#### SOLUTION

Solution :

997×998=(10003)(10002)
=100023×10002×1000+(3)(2)
=[10000005000+6]=995006

(x+y)(xy)(x2+y2) = ___________.

A.

x3y3

B.

x3+y3

C.

x4+y4

D.

x4y4

#### SOLUTION

Solution : D

To simplify : (x+y)(xy)(x2+y2)

Using the identity,
(a+b)(ab)=a2b2

we get,
(x+y)(xy)(x2+y2)
=(x2y2)(x2+y2)

Using the same identity again,
where a=x2 and b=y2,

we get,

(x2y2)(x2+y2)
=(x2)2(y2)2
=x4y4

Simplify (x+3)(x+5).

A.

x2+6x+9

B.

x2+8x+15

C.

x2+9x+6

D.

9x2+6x+9

#### SOLUTION

Solution : B

To simplify: (x+3)(x+5)

Using the identity  [(x+a)(x+b)2=x2+(a+b)x+ab]
we get,

(x+3)(x+5)=x2+(3+5)x+3×5=x2+8x+15

Which of the following are like terms to 9pq2?

A. 8ab
B. 5bc
C.

5q2p

D.

12pq2

#### SOLUTION

Solution : C and D

Like terms are terms with the same variables raised to the same power. Coefficients of like terms need not be the same.
5q2p=5pq2.
Hence 5q2p and 12pq2 are both correct answers.

3xy25y25x15 is an example of trinomial.

A.

True

B.

False

#### SOLUTION

Solution : B

Expressions that contain exactly three terms are called trinomials. The given expression has four terms. Hence,the given statement is false.

The area of a rectangle having length and width as 5xy and 9y respectively is 45xy.

A.

True

B.

False

#### SOLUTION

Solution : B

Area of a rectangle = length × width

Area = 5xy×9y

= 45xy2

Hence the given statement is false.

The product of (t+s2) and (t2s) is

A.

t3+s2t2sts3

B.

t3+s2t2sts2

C.

t3+s2t22sts3

D.

t3+t2sts3

#### SOLUTION

Solution : A

(t+s2)(t2s)=[t(t2s)+s2(t2s)]

=t3ts+s2t2s3

=t3+s2t2sts3