Handling Parentheses in Algebraic Expressions

This page focuses on the rules for removing parentheses in algebraic expressions, an essential skill for simplifying equations.

Parentheses Preceded by a Plus Sign

When parentheses are preceded by a plus sign, they can be removed without changing the expression inside.

Rule: For expressions like a + $b + c$, simply remove the parentheses: a + b + c.

Example: 5 + $2x + 3x - 4$ = 5 + 2x + 3x - 4

This rule applies even in the absence of explicit development.

Parentheses Preceded by a Minus Sign

To remove parentheses preceded by a minus sign, change the sign of each term inside the parentheses.

Rule: For expressions like a - $b + c$, remove the parentheses and change signs: a - b - c.

Example: 6x - $-2x - 3$ = 6x + 2x + 3 = 8x + 3

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Algebraic Calculations for Brevet Exam

This page introduces fundamental concepts in algebraic calculations, crucial for the French Brevet exam. It covers three main topics: reducing algebraic expressions, developing products, and the distributive property.

Reducing Algebraic Expressions

Reducing an algebraic sum involves decreasing the number of terms by combining like terms.

Definition: Reducing an algebraic sum means combining terms of the "same nature" to simplify the expression.

Example: 5x² - 3x² + 3x - 9x + 6x + 15 - 3 = 2x² + 0x + 12

Developing Products

Developing a product means transforming it into a sum using the distributive property.

Vocabulary: The distributive property is expressed as k$a + b$ = ka + kb, where k is the factor of $a + b$.

Example: A = 5$x + 3$ = 5x + 15

Highlight: For more complex expressions, the distributive property can be applied multiple times, as in B = 2x$4 + 3x$ = 8x + 6x².

The page also covers the distributive property for subtraction: k$a - b$ = ka - kb.

Example: D = -4x²$6x + 9$ = -24x³ - 36x²

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