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Percentages

• Increase and Decrease Calculations:
  • Increase a number by a percentage:
    $\text{Increase } 25\text{ by } 40\%: \frac{40 \times 25}{100} = 10$
    So, new value is $25 + 10 = 35$.
  • Decrease a number by a percentage:
    $\text{Decrease } 150\text{ by } 20\%: \frac{20 \times 150}{100} = 30$
    So, new value is $150 - 30 = 120$.

Algebraic Expressions

• Rules for Like Terms:
  • Like terms: terms with exact same variables and exponents.
  • Example of like terms: $20c, 5c, 6c$.
• Combining Like Terms:
  • Example: $2x + 5c + 6x = 8x + 5c$.
  • Maintain order (alphabetical).

Simplification of Algebraic Expressions

• Basic Addition and Multiplication:
  • Example: $x + x + x = 3x$.
  • E.g., $2x + 3x + x = 6x$.
• Combination of variables:
  • Keep track of coefficients.
  • Simplifying expressions with mixed variables.

Multiplication of Algebraic Expressions

• Multiplying Monomials:
  • Step 1: Multiply coefficients.
  • Step 2: Apply the law of exponents for variables.
  • Example:
  • $(-7x)(-4y) = 28xy$.

Operations Involving Monomials

• Using distributive property for multiplication:
  • Example:
  • Simplifying combinations such as $50c^3 + 10x^2$ or others using laws of exponents.
• Exponent Basics:
  • Use laws of exponents when multiplying or dividing terms.