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Question:

Factorise the following using appropriate identities:
(i) 9x² + 6xy + y²
(ii) 4y² - 4y + 1
(iii) x² - y²/100

Solution:

(i) 9x² + 6xy + y² = (3x)² + 2(3x)(y) + (y)² = (3x + y)²
(ii) 4y² - 4y + 1 = (2y)² - 2(2y)(1) + 1² = (2y - 1)²
(iii) x² - y²/100 = (x)² - (y/10)² = (x - y/10)(x + y/10)