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Worked Example: Squaring a Bracket

Expand: (x + 3)²

Key Rewrite as double brackets

(x + 3)² = (x + 3)(x + 3)

DON'T just square each term! It's NOT x² + 9

FOIL Apply FOIL method

F: x² | O: 3x | I: 3x | L: 9

x² + 3x + 3x + 9

Final Simplify

= x² + 6x + 9

Pattern: (a + b)² = a² + 2ab + b²

Q5 Expand: (x + 3)(x + 5) [2 marks]

[1] F: x², O: 5x, I: 3x, L: 15

[1] x² + 5x + 3x + 15 = x² + 8x + 15

Q6 Expand: (x + 3)(x - 4) [2 marks]

[1] F: x², O: -4x, I: 3x, L: -12

[1] x² - 4x + 3x - 12 = x² - x - 12

Q7 Expand: (x + 5)² [2 marks]

[1] (x + 5)² = (x + 5)(x + 5)

[1] x² + 5x + 5x + 25 = x² + 10x + 25

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