Advanced Expanding Brackets Techniques

This page delves into more complex examples of expanding brackets, including scenarios with higher degree polynomials and multiple sets of brackets.

The first example demonstrates expanding brackets with a quadratic term:

(x + 2)(x² + x + 3) = x³ + 3x² + 5x + 6

Highlight: When expanding brackets with higher degree terms, be careful to correctly multiply the exponents.

The page then shows an example with two sets of brackets, each containing multiple terms:

(2x - 1)(7x² + x - 5) = 14x³ + 2x² - 10x - 7x² - x + 5 = 14x³ - 5x² - 11x + 5

This example illustrates the importance of methodically multiplying each term and carefully combining like terms.

Example: (3x + 1)(x + 1) + 2(x² - 5) = 3x² + 5x² + 4x - 9

This problem combines expanding brackets with additional operations, demonstrating how these skills are applied in more complex algebraic expressions.

The page concludes with two more examples:

(2x - 5)(3x + 1) = 6x² - 13x - 5

(x - 4)(x² + x - 2) = x³ + x² - 2x - 4x² - 4x + 8 = x³ - 3x² - 6x + 8

Vocabulary: Polynomial - An expression consisting of variables and coefficients, involving only addition, subtraction, and multiplication operations.

These final examples reinforce the techniques for expanding double brackets and handling more complex algebraic expressions.

Highlight: Practice is key to mastering the skill of expanding brackets. Use expanding brackets worksheets and expanding brackets examples for algebra practice to improve your proficiency.

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.