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QUESTION: 1

Which of the following is an expression?

Solution:
(c) Becoz highest power of variable 'x' is not equal to zero . ..

QUESTION: 2

Which of the following is a binomial?

Solution:

An algebraic expression consisting of unlike terms is called a binomial.

so, 2x+7 is a binomial as it contains two unlike terms i.e 2x and 7.

QUESTION: 3

Expressions consists of _____________ and _______________.

Solution:
Variables and constants .This is because an expression is made up of these only.

QUESTION: 4

What degree does x^{3} - x^{2}y^{2} - 8y^{2}+ 2 have?

Solution:

Monomial means expression containing only one term and option B has one term so it is a monomial.

QUESTION: 5

When numbers/literals are added or subtracted, they are called _________.

Solution:

QUESTION: 6

Multiply (a + 7) and (b – 5).

Solution:

(a+7)(b-5) = a(b-5)+7(b-5) = ab-5a+7b-35

QUESTION: 7

Simplify: (x + y) (2x – 3y + z) – (2x – 3y)z

Solution:

QUESTION: 8

If (x+1/x) = 6, find x^{2}+1/x^{2}

Solution:
X²+1/x² can be written as (x+1/x)²-2 on putting values we have 6²-2=34

QUESTION: 9

Solution:

QUESTION: 10

Which of the following is an expression?

Solution:
Option C is correct bcuz, an expression consists of at least one variable like :- x, y, z as well as a number.
An expression can also be like this :- 2xy, 3y², 5xy+8, 6z²-3, etc

QUESTION: 11

Which of the following is a trinomial?

Solution:
Because monomial 1 term binomial, 2 terms and trinomial 3 terms therefor 7_3x+4y trinomial.

QUESTION: 12

Which of the following is like term as 3xy^{2}?

Solution:

QUESTION: 13

Subtract 3x (x – 4y + 5z) from 4x (2x – 3y + 10z).

Solution:

QUESTION: 14

n (4 + m) = 4n + ___

Solution:
N(4+m) = 4n + ___Here , n is multiplied by 4 which is added to n multiplied by m.so, n×4= 4n n×m= nm so the answer is 4n + nm.

QUESTION: 15

Using identity evaluate 297 × 303.

Solution:

297×303

(300-3)(300+3)

(300)whole square (3)whole square

90000-9

89991. identity

{a-b} {a+b} ={a square} - {b square}

QUESTION: 16

Simplify: (1.5x – 4y)(1.5x + 4y +3) – 4.5x +12y

Solution:

(1.5x - 4y) (1.5x + 4y + 3) - 4.5x + 12y

= 1.5x(1.5x + 4y +3) - 4y(1.5x + 4y +3) - 4.5x +12y

= (1.5x X 1.5x) + (1.5x X 4y) + (1.5x X 3) - (4y X 1.5x) - (4y X 4y) - (4y x 3) - 4.5x +12y

= 2.25x^2 + 6xy + 4.5x - 6xy - 16y^2 - 12y - 4.5x + 12y

= 2.25x^2 + ( 6 - 6)xy + (4.5 - 4.5)x - 16y^2 + (12 - 12)y

= 2.25x^2 + 0 + 0 - 16y^2 + 0

= 2.25x^2 - 16y^2

QUESTION: 17

If x + y = 12 and xy = 32, find the value of x^{2}+ y^{2}.

Solution:

x=8 or 4 and y=4 or 8 so,x^2+y^2=64 +16 or 16 +64 =80 and that is option A.

QUESTION: 18

(x – a) (x + a) = ?

Solution:
(a-b)(a+b) = a^2 - b^2(x-a)(x+a) = x (x+a) -a (x+a) = x^2 + ax -ax -a^2 = x^2 - a ^2

QUESTION: 19

Which of the following is a trinomial?

Solution:

QUESTION: 20

If x = 3 is solution of x² + kx + 15, value of k is

Solution:

Since solution is x=3, this means the equation is equal to 0 when x=3, substituting the values gives k=-8

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