2.5.1 Expanding Brackets

Expanding brackets is a fundamental algebraic technique used to simplify expressions by removing parentheses (brackets) and combining like terms. This skill is essential for solving equations, simplifying expressions, and working with polynomials.

1. Expanding a Single Bracket

When you expand a single bracket, you distribute the term outside the bracket to each term inside the bracket.

General Form: $a(b + c) = ab + ac$

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Example: $3(x + 4) = 3 \times x + 3 \times 4 = 3x + 12$

2. Expanding Double Brackets

Expanding double brackets involves multiplying two binomials (expressions with two terms). The most common method is the FOIL method (First, Outside, Inside, Last).

General Form: $(a + b)(c + d) = ac + ad + bc + bd$

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FOIL Method:

First: Multiply the first terms from each bracket.
Outside: Multiply the outer terms.
Inside: Multiply the inner terms.
Last: Multiply the last terms.

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Example: $(x + 2)(x + 3)$

First: $\ x \times x = x^2$
Outside: $\ x \times 3 = 3x$
Inside: $\ 2 \times x = 2x$
Last: $\ 2 \times 3 = 6$ Combine the results: $x^2 + 3x + 2x + 6 = x^2 + 5x + 6$

3. Expanding with Negative Signs

When dealing with negative signs, be careful with the distribution to ensure correct signs in the expanded expression.

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Example: $(2x - 3)(x + 4)$

First: $\ 2x \times x = 2x^2$
Outside: $\ 2x \times 4 = 8x$
Inside: $\ -3 \times x = -3x$
Last: $\ -3 \times 4 = -12$ Combine the results: $2x^2 + 8x - 3x - 12 = 2x^2 + 5x - 12$

4. Expanding with More Than Two Brackets

When expanding more than two brackets, expand two brackets first, then multiply the result by the remaining bracket(s).

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Example: $(x + 1)(x - 2)(x + 3)$

First, expand $\ (x + 1)(x - 2) = x^2 - x - 2 .$
Then, multiply this result by $\ (x + 3)$ : $(x^2 - x - 2)(x + 3) = x^3 + 3x^2 - x^2 - 3x - 2x - 6 = x^3 + 2x^2 - 5x - 6$

Summary:

Single Bracket: Distribute the outer term across the inner terms.
Double Brackets: Use the FOIL method to ensure all terms are multiplied correctly.
Negative Signs: Pay close attention to signs when distributing.
Multiple Brackets: Expand in pairs, then combine results.

Expanding Brackets Simplified Revision Notes for A-Level OCR Maths Pure

2.5.1 Expanding Brackets

1. Expanding a Single Bracket

2. Expanding Double Brackets

3. Expanding with Negative Signs

4. Expanding with More Than Two Brackets

Summary:

500K+ Students Use These Powerful Tools to Master Expanding Brackets For their A-Level Exams.

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