Question
Factorise:
4a2 - 4b2 + 4a + 1
4a2 - 4b2 + 4a + 1
✓
Answer
4a2 - 4b2 + 4a + 1
= (4a2 + 4a + 1) - 4b2
= [(2a)2 + 2 × 2a × 1 + (1)2] - (2b)2
= (2a + 1)2 - (2b)2
= (2a + 1 - 2b)(2a + 1 + 2b)
= (2a - 2b + 1)(2a + 2b + 1)
= (4a2 + 4a + 1) - 4b2
= [(2a)2 + 2 × 2a × 1 + (1)2] - (2b)2
= (2a + 1)2 - (2b)2
= (2a + 1 - 2b)(2a + 1 + 2b)
= (2a - 2b + 1)(2a + 2b + 1)
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