HOW TO WRITE EACH EXPRESSION AS A PRODUCT OF ITS FACTORS

List all the Factors of the monomial expression

Problem 1 :

a)  6ab²

b)  52w

c)  2r³s

d)  7xyz

Solution :

Decompose each expression into prime factors.

a)  6ab² = 2 ∙ 3  ∙ a  ∙ b ∙ b

b)  52w = 2 ∙ 2 ∙ 13 ∙ w

c)  2r³s = 2 ∙ r ∙ r ∙ r ∙ s

d)  7xyz = 7 ∙ x ∙ y ∙ z

Finding the degree, coefficient and variables of following monomial expression

Variables :

The variables are the letters present in a monomial. That is, x, y, z,.. 

Coefficient :

The coefficient is the number that is multiplied by the variables. That is, 12x, 12y,..

Degree :

The degree is the sum of the exponents of the variables in a monomial.

That is, 12xy ---> Exponent of x is 1, Exponent of y is 1

So, the degree is 1 + 1 = 2

Problem 2 :

a)  11cd

b)  19m3

c)  3f6

d)  21ab

e)  5xy2

f)  35rs5

g)  2y4z3

h)  40m2n

Solution :

a)  

Coefficient : 11

Variables : c, d

Degree : 2

e)

Coefficient : 5

Variables : x, y

Degree : 3

b)

Coefficient : 19

Variable : m

Degree : 3

f)

Coefficient : 35

Variables : r, s

Degree : 6

c)  

Constant : 3

Variable : f 

degree : 6

g)

Coefficient : 2

Variables : y, z

Degree : 7


d)

Coefficient : 21

Variables : a, b

Degree : 2 

h)

Coefficient : 40

Variables : m, n

Degree : 3

Find the Greatest Common Factors of the following Monomial expression

Problem 3 :

12m²n³, 70m³n

Solution :

Find the GCF of 12m²n³, 70m³n.

12m²n³ = ∙ 2 ∙ 3 ∙ ∙ ∙ n ∙ n ∙ n

70m³n = ∙ 5 ∙ 7∙ ∙ ∙ m ∙ n

= 2 ∙ m ∙ m ∙ n

GCF = 2m²n

Problem 4 :

72a³b², 86a

Solution :

Find the GCF of 72a³b², 86a.

72a³b² = ∙ 2 ∙ 2 ∙ 3 ∙ 3 . ∙ a ∙ a ∙ b ∙ b

86a = ∙ 43 ∙ a

GCF = 2a

Problem 5 :

44m²n, 48mn²

Solution :

Find the GCF of 44m²n, 48mn².

44m²n = ∙ ∙ 11 ∙ m ∙ n

48mn² = ∙ ∙ 2 ∙ 2 ∙ 3 ∙ ∙ ∙ n

 = 2 ∙ 2 ∙ m ∙ n

GCF = 4mn

Problem 6 :

a²b³, ab³

Solution :

a²b³ = ∙ a ∙ ∙ ∙ b

ab³ = ∙ ∙ ∙ b

= a ∙ b ∙ b ∙ b

GCF = ab³

Problem 7 :

3x, 7xy²

Solution:

3x = 3 ∙ x

7xy² = 7 ∙ ∙ y ∙ y 

GCF = x

Problem 8 :

4rs², 27st³

Solution:

4rs² = 2 ∙ 2 ∙ r ∙ ∙ s

27st³ = 3 ∙ 3 ∙ 3 ∙ ∙ t ∙ t ∙ t

GCF = s

Problem 9 :

18wx², 45wx

Solution:

18wx² = 2 ∙ ∙ ∙ ∙ ∙ x

45wx = ∙ ∙ 5 ∙ ∙ x

= 3 ∙ 3 ∙ w ∙ x

GCF = 9wx

Problem 10 :

12y², 15y³, 5y

Solution:

12y² = 2 ∙ 2 ∙ 3 ∙ ∙ y

15y³ = 3 ∙ 5 ∙ ∙ y ∙ y

5y = 5 ∙ y

GCF = y

Problem 11 :

rs³, s³t, r²st²

Solution :

rs³ = r ∙ ∙ s ∙ s

s³t = ∙ s ∙ s ∙ t

r²st² = r ∙ r ∙ ∙ t ∙ t

GCF = s

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