PRACTICE ON ALGEBRAIC EXPRESSION

Problem 1 :

Write the expression for the statement: the sum of three times x and 11?

a) x + 3 + 11   b) 3x + 11    c) 3 + 11x    d) 3x - 11

Solution :

Let the number be x. Three times a number is 3x.

= 3x + 11

So, option (b) is correct.

Problem 2 :      

Identify the coefficient of x in expression 8 - x + y

a) 0        b) 8        c) -1       d) 1

Solution :

The coefficient of x in expression 8 - x + y

Coefficient of x is -1.

So, option (c) is correct.

Problem 3 :

The number of terms in 4p²q - 3pq² + 5 is:     

a) 7       b) 3        c) 1       d) 4

Solution :

4p²q - 3pq² + 5

Number of terms: 3

So, option (b) is correct.

Problem 4 :

The expression for sum of numbers a and b subtracted from their product is

a) a + b - ab           b) ab - a + b

c) ab - (a + b)        d) ab + a - b

Solution :

Sum of a and b is (a + b)

Product is a ∙ b

(a + b) subtract from ab

ab - (a + b)

So, option (c) is correct.

Problem 5 :

What is the numerical coefficient of y² in the expression 2x²y - 15xy² + 7y?

a) -15x     b) -15      c) 2      d) 7

Solution :

Numerical coefficient of y² in the expression 2x²y - 15xy² + 7y is -15x

So, option (a) is correct.

Problem 6 :

The expression x + y - xy is:

a) Monomial    b) Binomial     c) Trinomial    d) Quadrinomial

Solution :

Given polynomial is x + y - xy

The variables are x and y

Since the polynomial consists of three terms

So, the given polynomial is a trinomial.

So, option (c) is correct.

Problem 7 :

The expression xyz is:

a) Monomial    b) Binomial

c) Trinomial     d) Zero polynomial

Solution :

Given polynomial is xyz

The polynomial consists of one term

So, the given polynomial is a monomial.

So, option (a) is correct.

Problem 8 :

From the following expressions

10pq, 7p, 8q, -7pq, -23, ab, 3a, b

The like terms

a) 3, 7p      b) 10pq, -7pq    c) ab, 3a, b      d) 10pq, 7p, 8q

Solution :

Like terms means, we should have same set of variables.

In option b, for both terms we have same variables pq.

10pq, -7pq

So, option (b) is correct.

Problem 9 :

From the following expressions

3ab, a², b², a, 5ab, -2ab, 2a²

the three like terms are :

a) 3ab, 5ab, -2ab     b) a², a, 2a²

c) 3ab, a², b²           d) 2a², a², a

Solution :

Three like terms are 3ab, 5ab, -2ab

So, option (a) is correct.

Problem 10 :

The value of 21b - 32 + 7b - 20b is:

a) 48b - 32      b) -8b - 32      c) 8b - 32     d) 28b - 52

Solution :

= 21b - 32 + 7b - 20b

= 28b - 20b - 32

= 8b - 32

So, option (c) is correct.

Problem 11 :

The value of expression 7a - 4b for a = 3, b = 2 is:

a) 13      b) 7a - 6b        c) 21a - 8b     d) 29

Solution :

= 7a - 4b

= 7(3) - 4(2)

= 21 - 8

= 13

So, option (a) is correct.