Exercise 1

Indicate which of the following expressions are monomials. If it is, indicate the degree and coefficient of the monomial. If it is not, state why it is not a monomial:

3x^3

5x ^ {-3}

3x + 1

\sqrt{2} x

- \frac{3}{4} x^{4}

-\frac {3}{x^4}

2 \sqrt{x}

 

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Exercise 2

Simplify:

1   2 x^2y^3z + 3x^2y^3z

2   2x^3 - 5x^3

3x^4 - 2x^4 + 7x^4

2a^2bc^3 - 5a^2bc^3 + 3a^2bc^3 - 2a^2bc^3

Exercise 3

Solve:

1   (2x^3) \cdot (5x^3)

2   (12x^3) \cdot (4x)

3   5 \cdot (2x^2y^3z)

4   (5x^2y^3z) \cdot (2y^2z^2)

5   (18x^3y^2z^5) \cdot (6x^2yz^2)

6   (-2x)^3) \cdot (-5x) \cdot (-3x^2)

Exercise 4

Solve:

(12x^3) : (4x)

(18x^6y^2z^5) : (6x^3yz^2)

(36x^3y^7z^4) : (12x^2y^2)

\frac {6x^3y^4z^2} {3x^2y^2z^2}

\frac{24x^5y^4 + 18x^4y^5 - 48x^{10}y^3} {6x^2y^3}

\frac{12x^3y^5 + 18x^5y^7 - 48x^{12} y^6} {3x^2y^2}

 

Exercise 5

Solve:

(2x^3)^3

(-3x^2)^3

(\frac{2}{3} x^3 )^2

 

 

 

Solution of exercise

Solution of exercise 1

 

Indicate which of the following expressions are monomials. If it is, indicate the degree and coefficient of the monomial. If it is not, state why it is not a monomial:

3x^3

Degree : 3, coefficient : 3

 

5x ^ {-3}

It is not a monomial because the exponent is not a natural number

 

3x + 1

It is a binomial, not a monomial.

 

\sqrt{2} x

Degree : 1, coefficient \sqrt{2}

 

- \frac{3}{4} x^{4}

Degree:4, coefficient : \frac{3}{4}

 

-\frac {3}{x^4}

It is not a monomial because the exponent is not a natural number.

 

2 \sqrt{x}

It is not a monomial because the variable is inside the root.

 

Solution of exercise 2

Simplify:

1   2x^2y^3z + 3x^2y^3z = 5x^2y^3z

 

2x^3 - 5x^3 = -3x^3

 

3x^4 - 2x^4 + 7x^4 = 8x^4

 

2a^2bc^3 - 5a^2bc^3 + 3a^2bc^3 - 2a^2bc^3 = -2a^2bc^3

 

Solution of exercise 3

Solve:

1   (2x^3) \cdot (5x^3) = 10x^3

 

2   (12x^3) \cdot (4x) = 48x^4

 

3   5 \cdot (2x^2y^3z) = 10x^2y^3z

 

4   (5x^2y^3z) \cdot (2y^2z^2) = 10x^2y^5z^3

 

5   (18x^3y^2z^5) \cdot (6x^2yz^2) = 108x^6y^3z^7

 

6   (-2x)^3) \cdot (-5x) \cdot (-3x^2) = -30x^6

 

Solution of exercise 4

Solve:

(12x^3) : (4x) = 3x^2

 

(18x^6y^2z^5) : (6x^3yz^2) = 3x^3yz^3

 

(36x^3y^7z^4) : (12x^2y^2) = 3xy^5z^4

 

\frac {6x^3y^4z^2} {3x^2y^2z^2} = 2xy^2

 

\frac{24x^5y^4 + 18x^4y^5 - 48x^{10}y^3} {6x^2y^3} = 4x^3y + 3x^2y^2 - 8x^8

 

\frac{12x^3y^5 + 18x^5y^7 - 48x^{12} y^6} {3x^2y^2} = 4xy^3 + 6x^3y^5 - 16x^{10}y^4

 

Solution of exercise 5

Solve:

(2x^3)^3 = 8x^9

 

(-3x^2)^3 = -27x^6

 

(\frac{2}{3} x^3 )^2 = (\frac{2}{3})^2 (x^3)^2 = \frac{4}{9} x^6

 

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.