IDENTIFYING PARTS OF AN EXPRESSION WORKSHEET

Identify the terms and their factors in the following expressions Show the terms and factors by tree diagrams.

Problem 1 :

x – 3

Solution

Problem 2 :

1 + x + x²

Solution

Problem 3 :

5xy² + 7x² y

Solution

Problem 4 :

– ab + 2b² – 3a²

Solution

Problem 5 :

Identify the numerical coefficients of terms (other than constants) in the following expressions:

(i) 5 – 3t²

(ii) 1 + t + t² + t³

(iii) x + 2xy + 3y

Solution

Problem 6 :

Classify into monomials, binomials and trinomials.

(i) 4y – 7z

(ii) y²

(iii) x + y – xy

(iv) 100

(v) ab – a – b

Solution

Problem 7 :

State whether a given pair of terms is of like or unlike terms.

(i) 1, 100

(ii) –7x, 52x

(iii) – 29x, – 29y

(iv) 14xy, 42yx

(v) 4m²p, 4mp²

Solution

Problem 8 :

If A = 3x² – 4x + 1, B = 5x² + 3x – 8 and C = 4x² – 7x + 3

then find :

(i) (A + B) – C

(ii) B + C – A

(iii) A + B + C

Solution

Problem 9 :

If P = –(x – 2), Q = –2(y +1) and R = –x + 2y, find a, when P + Q + R = ax.

Solution

Problem 10 :

From the sum of x² – y² – 1, y² – x² – 1 and 1 – x² – y² subtract – (1 + y²)

Solution

Problem 11 :

Subtract the sum of 12ab –10b² –18a² and 9ab + 12b² + 14a² from the sum of ab + 2b² and 3b² – a².

Solution

Answer Key

1) 

2)

3)

4) 

Factors of -ab is -1, a and b.

Factors of 2b² is 2, b and b.

Factors of -3a² is -1, 3, a and a.

5)

 i) Coefficient of t² is -3.

ii)

• Coefficient of t is 1.
• Coefficient of t² is 1.
• Coefficient of t³ is 1.

(iii) 

• Coefficient of x is 1.
• Coefficient of xy is 2.
• Coefficient of y is 3.

6) 

(i) Consists of 2 terms, so it is binomial.

(ii) Consists of 1 term, so it is monomial.

(iii) Consists of 3 terms, so it is trinomial.

(iv) Consists of 1 term, so it is monomial.

(v) Consists of 3 terms, so it is trinomial.

7) 

(i) 1, 100 - like terms

(ii) –7x, 52x - like terms

(iii) – 29x, – 29y - unlike terms

(iv) 14xy, 42yx - like terms

(v) 4m²p, 4mp² - unlike terms

8) i) 4x²  + 6x - 10

ii)  6x² - 6

iii) 12x² – 8x - 4

9)  a = -2.

10) – x² – 2y²  – 1 

11)  - 20ab + 3b² + 3a²

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

Problem 2 :

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

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

Solution

Problem 3 :

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

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

Solution

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

Problem 5 :

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

Solution

Problem 6 :

The expression x + y - xy is:

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

Solution

Problem 7 :

The expression xyz is:

a) Monomial    b) Binomial

c) Trinomial     d) Zero polynomial

Solution

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

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

Problem 10 :

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

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

Solution

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

Problem 12 :

A wire is (7x – 3) meters long. A length of (3x – 4) meters 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

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

Problem 14 :

Product of 6a² – 7b + 5ab and 2ab is

Solution

Problem 15 :

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

Solution