This study notes covers Worked Examples within Quadratic Expressions for GCSE Mathematics. Revise Quadratic Expressions in Algebra for GCSE Mathematics with 12 exam-style questions and 22 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 5 of 8 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 5 of 8
Practice
12 questions
Recall
22 flashcards
Worked Examples
Example 1: Basic Expansion
Expand: (x + 2)(x + 6)
Solution:
Using FOIL:
First: x × x = x²
Outer: x × 6 = 6x
Inner: 2 × x = 2x
Last: 2 × 6 = 12
Answer: x² + 8x + 12
Example 2: Expansion with Negatives
Expand: (x + 4)(x - 3)
Solution:
First: x × x = x²
Outer: x × (-3) = -3x
Inner: 4 × x = 4x
Last: 4 × (-3) = -12
Answer: x² + x - 12
Example 3: Perfect Square
Expand: (x + 5)²
Solution:
(x + 5)² = (x + 5)(x + 5)
First: x × x = x²
Outer: x × 5 = 5x
Inner: 5 × x = 5x
Last: 5 × 5 = 25
Answer: x² + 10x + 25
Example 4: Difference of Squares
Expand: (x + 7)(x - 7)
Solution:
First: x × x = x²
Outer: x × (-7) = -7x
Inner: 7 × x = 7x
Last: 7 × (-7) = -49
The middle terms cancel: -7x + 7x = 0
Answer: x² - 49
Example 5: Basic Factorising
Factorise: x² + 9x + 20
Solution:
Need two numbers that add to 9 and multiply to 20
Factors of 20: 1×20, 2×10, 4×5
Check sums: 1+20=21 ✗, 2+10=12 ✗, 4+5=9 ✓
Answer: (x + 4)(x + 5)
Example 6: Factorising with Negatives
Factorise: x² - 5x - 14
Solution:
Need two numbers that add to -5 and multiply to -14
One positive, one negative number needed
Factors of 14: 1×14, 2×7
Try: 2 + (-7) = -5 ✓ and 2 × (-7) = -14 ✓
Answer: (x + 2)(x - 7)
Keep building this topic
Read this section alongside the surrounding pages in Quadratic Expressions. That gives you the full topic sequence instead of a single isolated revision point.
Practice Questions for Quadratic Expressions
Expand (x + 5)².
Explain how to recognise whether x² + 12x + 36 is a perfect square trinomial, and write it in factorised form.
Quick Recall Flashcards
12 questions on Quadratic Expressions — practise free
Instant marking, adaptive difficulty, and 22 spaced repetition flashcards. Free until your GCSEs.
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