The Snail's House

Snail's Behavior

• The snail sticks to surfaces like grass, leaves, fruits, or walls, and is not afraid of falling.
• The snail appears to be a part of its surroundings, as if it were a permanent fixture.

Self-Protection

• When faced with danger or bad weather, the snail retreats into its shell for protection.
• The snail's shell provides a secure hiding place.

Defensive Mechanism

• If the snail's horns are touched, it will quickly retreat into its shell, displaying displeasure.
• The snail has a strong instinct to protect itself by withdrawing into its shell.

Social Behavior

• The snail is a solitary creature, living alone without any companions.
• The snail is content with its own company and has no need for external possessions or relationships.

Algebraic Expressions

• To find the product of 3% and √3, multiply the coefficients and simplify the radicals.
• To find the value of x in the equation 2√2 × k = 4, divide both sides by 2√2 and simplify.
• To find the product of 3/5 and 5/3, multiply the numerators and multiply the denominators, then simplify.

Multiplication of Algebraic Expressions

• To multiply algebraic expressions, multiply each term in the first expression by each term in the second expression, and combine like terms.
• Examples of multiplication of algebraic expressions:
  • √7 × 14 = √(7 × 14) = √98
  • √12 × 2√3 = √(12 × 4 × 3) = √144
  • √5 × 15 × √3 = √(5 × 15 × 3) = √675
  • (√2 + √3) (√2 - √3) = 2 - 3 = -1
  • (√3 + 1) (3 - 1) (2 - 3) (4 + 2√3) = 2 × 2 × (-1) × (4 + 2√3) = -16 - 8√3

Simplification of Algebraic Expressions

• To simplify an algebraic expression, combine like terms and simplify the radicals.
• Examples of simplification of algebraic expressions:
  • √5 - 3 = √(5 - 9) = √(-4) = 2i
  • 3/2 + 3 = 9/2
  • 7 + √48 = 7 + 4√3
  • (√5 + 2) - 3 = √5 - 1
  • (√3 + √2) + √7 = √(3 + 2 + 7) = √12

Factorization of Algebraic Expressions

• To factorize an algebraic expression, find the greatest common factor (GCF) of the terms and divide each term by the GCF.
• Examples of factorization of algebraic expressions:
  • 9 - 4/5 = (9/5) - (4/5) = (5/5) = 1
  • -2 - √7 = -2 - √(7) = -2 - √(4 + 3) = -2 - 2i
  • √3 + √2 + √7 = √(3 + 2 + 7) = √12
  • √8 - 3 = √(8) - 3 = 2√2 - 3

Mixed Quadratic Equations

• To solve a mixed quadratic equation, factorize the equation and solve for the variable.
• Examples of mixed quadratic equations:
  • 9 - 4/5 = 0 => (5/5) = 0 => 1 = 0 => no solution
  • -2 - √7 = 0 => -2 - 2i = 0 => 2i = 2 => i = 1 (no real solution)
  • √3 + √2 + √7 = 0 => √(3 + 2 + 7) = 0 => √12 = 0 => no real solution
  • √8 - 3 = 0 => 2√2 - 3 = 0 => 2√2 = 3 => √2 = 3/2 => 2 = 9/4 => 8 = 9 => no real solution