Question

Factorise the following using appropriate identities : 

(i) 9x² + 6xy + y² 

(ii) 4y² – 4y + 1 

(iii) x² - \(\frac{y^2}{100}\)

Answer 1

(i) 9x² + 6xy + y² 

= (3x)² + 2(3x)(y) + (y)² 

= (3x + y)² [∵ x² + 2xy + y² = (x + y)²] 

(ii) 4y² – 4y + 1 

= (2y)² – 2(2y)(1) + (1)² 

= (2y – 1)² [∵ x² – 2xy + y² = (x – y)²]