Expanding Brackets in Algebra
This page provides a comprehensive guide on expanding brackets in algebra, covering both single and double bracket expansions. The content is essential for students learning algebraic manipulation techniques.
The worksheet begins by demonstrating how to expand brackets in algebra with single bracket examples. It shows that when expanding a single bracket, each term inside the bracket is multiplied by the term outside.
Example: 3(x+2) = 3x + (3×2) = 3x + 6
Another example illustrates the expansion of a bracket with a variable term outside:
Example: 4x(y + 3) = 4xy + 12x
The document then progresses to expanding double brackets, which is a more complex operation. It demonstrates that when expanding double brackets, each term in the first bracket must be multiplied by each term in the second bracket.
Example: (x + 3)(x + 9) = x² + 9x + 3x + 27
A second example of double bracket expansion is provided:
Example: (x + 2)(3y + 6) = 3xy + 6x + 2y + 6
Highlight: The worksheet emphasizes that expanding double brackets can be useful for solving equations by finding their roots.
The final section explains how to use expanded double brackets to find the roots of an equation:
Example: If (x + 3)(x + 9) = 0, then either x + 3 = 0 or x + 9 = 0, leading to the roots x = -3 or x = -9.
This comprehensive coverage of expanding brackets examples and techniques provides students with a solid foundation for more advanced algebraic operations.
