Expanding Brackets: Basic to Advanced Examples
This page introduces the concept of expanding brackets in algebra, providing a range of examples from simple to complex. Expanding brackets is a crucial skill in algebra, used to simplify expressions and solve equations.
Definition: Expanding brackets means multiplying the term outside the brackets by each term inside, then combining like terms.
The page starts with a simple example:
5(x + 4) + 3(2x + 1) = 5x + 20 + 6x + 3 = 11x + 23
This example demonstrates the basic process of distributing the outside term to each term inside the brackets, then combining like terms.
Example: x(3x + 4) = 3x² + 4x
This shows how to expand when the outside term is a variable.
The page then progresses to more complex examples, including expanding double brackets:
Example: (x + 2)(x + 5) = x² + 7x + 10
This illustrates the FOIL method (First, Outer, Inner, Last) for expanding double brackets, which is a key technique in expanding double brackets.
Highlight: When expanding double brackets, remember to multiply each term in the first bracket by each term in the second bracket.
The page also includes examples with negative terms:
6x(-2 + 3) = -12x + 18x = 6x
(-x + 6)(3x - 5) = -3x² + 23x - 30
These examples emphasize the importance of careful sign management when expanding brackets with negative terms.
Vocabulary: FOIL - A method for expanding double brackets, standing for First, Outer, Inner, Last.
