Page 1: Basic Algebraic Operations
This page introduces fundamental algebraic operations essential for Développer et réduire 3ème level mathematics. It covers reducing expressions, removing parentheses, expanding, and factoring.
Definition: Reducing an algebraic expression means simplifying it by combining like terms.
The page begins with examples of reducing expressions:
5x2−6x+3 + −7x−2x2 = 3x² - 13x - 7
8x2−30x2 + 6ax - 40a² = -22x² + 6ax - 40a²
Example: When reducing 5x2−6x+3 + −7x−2x2, we combine like terms: 5x² and -2x² become 3x², -6x and -7x become -13x, and 3 remains as is.
Next, it demonstrates reducing expressions while removing parentheses:
-2x+3 + 7x−9 = -2x - 3 + 7x - 9 = 5x - 12
5x - −4x−7 - 9x+6 = 5x + 4x + 7 - 9x - 6 = 1
−5x - −7+3x = -5x + 7 + 3x = -2x + 7
Highlight: When removing parentheses, pay attention to the signs. A minus sign before parentheses changes all signs inside.
The page then moves on to expanding expressions:
5x4x+1 = 20x² + 5x
−5x × −7+3x = 35x - 15x² = -15x² + 35x
Vocabulary: Expanding an expression means multiplying each term inside the parentheses by the term outside.
Finally, it covers factoring:
3x - 3y = 3x−y
8x² + 5x = x8x+5
Definition: Factoring is the process of finding what you can multiply together to get the expression.