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.

Problem 12 :

A wire is (7x – 3) metres long. A length of (3x – 4) metres is cut for use. Now, answer the following questions:

(a) How much wire is left?

(b) If this left out wire is used for making an equilateral triangle. What is the length of each side of the triangle so formed?

Solution :

Length of the wire = 7x - 3 

Amount of wire cut = 3x - 4

a) Amount of wire left = 7x - 3 - (3x - 4)

= 7x - 3 - 3x + 4

= 4x + 1

b) Perimeter of equilateral triangle = 3(side length)

3(side length) = 4x + 1

Side length of equilateral triangle = (4x + 1)/3

Problem 13 :

Volume of a rectangular box (cuboid) with length = 2ab, breadth = 3ac and height = 2ac is

(a) 12a³bc²       (b) 12a³bc        (c) 12a²bc         (d) 2ab + 3ac + 2ac

Solution :

Volume of rectangular prism = length x width x height

length = 2ab, breadth = 3ac and height = 2ac

= 2ab(3ac)(2ac)

= 12a²bc²

Problem 14 :

Product of 6a² – 7b + 5ab and 2ab is

Solution :

= (6a² – 7b + 5ab)(2ab)

= 6a² (2ab) – 7b(2ab) + 5ab(2ab)

= 12a³b - 14ab² + 10a²b²

So, the answer is 12a³b - 14ab² + 10a²b^2.

Problem 15 :

If we subtract –3x²y² from x²y², then we get

Solution :

= x²y² - (–3x²y²)

= x²y² + 3x²y²

= 4x²y²

So, the answer is 4x²y².