ADIÇÃO, SUBTRAÇÃO, MULTIPLICAÇÃO e DIVISÃO | MONÔMIOS

Introduction

This tutorial focuses on performing basic operations with monomials, including addition, subtraction, multiplication, and division. Understanding these concepts is essential for mastering algebra and building a solid foundation in mathematics.

Step 1: Understanding Monomials

• A monomial is a mathematical expression consisting of a single term.
• It can include numbers, variables, and exponents, but must not have addition or subtraction.
• Example of a monomial: ( 3x^2 ) or ( -5y ).

Practical Tip

• Identify monomials by checking for a single term without any addition or subtraction.

Step 2: Adding Monomials

• To add monomials, combine like terms (terms with the same variable and exponent).
• Example:
  • ( 2x + 3x = (2 + 3)x = 5x ).
  • ( 4y^2 + 3y^2 = (4 + 3)y^2 = 7y^2 ).

Common Pitfall

• Ensure that the terms you want to add are indeed like terms; otherwise, they cannot be combined.

Step 3: Subtracting Monomials

• Subtraction of monomials is similar to addition. Combine like terms but subtract the coefficients.
• Example:
  • ( 5x - 2x = (5 - 2)x = 3x ).
  • ( 6y^2 - 4y^2 = (6 - 4)y^2 = 2y^2 ).

Step 4: Multiplying Monomials

• Multiply monomials by multiplying their coefficients and adding the exponents of like bases.
• Example:
  • ( 2x^2 \times 3x^3 = (2 \times 3)(x^{2+3}) = 6x^5 ).
  • ( -4y \times 2y^2 = (-4 \times 2)(y^{1+2}) = -8y^3 ).

Practical Tip

• Remember the rule: ( x^a \times x^b = x^{a+b} ).

Step 5: Dividing Monomials

• Divide monomials by dividing their coefficients and subtracting the exponents of like bases.
• Example:
  • ( \frac{6x^4}{2x^2} = \frac{6}{2}x^{4-2} = 3x^2 ).
  • ( \frac{-8y^3}{4y} = \frac{-8}{4}y^{3-1} = -2y^2 ).

Common Pitfall

• Make sure to subtract the exponents correctly; ( x^a / x^b = x^{a-b} ).

Conclusion

In this tutorial, we've covered the essential operations for working with monomials: addition, subtraction, multiplication, and division. Understanding these operations will enhance your algebra skills and prepare you for more advanced mathematical concepts. To further your studies, practice with different monomials and try solving equations that incorporate these operations. Keep exploring with the Método Curió for more structured learning!