Question

Fill in the blanks. 

(i) x² - 18 x + 81 = (…) 

(ii) 4 - 36x² = (…)(...) 

(iii) x² - 14x + 13 = (…)(…) 

(iv) 9z² - x² - 4y² + 4xy = (…)(…) 

(v) abc - ab - c + 1 = (…)(…)

Answer 1

Using the identity : a² – b² = (a + b)(a-b) 

(i) x² - 18x + 81 = x² - (9x) + 81 = (x - 9)(x - 9) = (x - 9)² 

(ii) (4 - 36 x²) = 4(1 - 9x²) = 4(1 - 3x)(1 + 3x) 

(iii) x² - 14x + 13 = x²–(13 + 1)x + 13 = x(x - 13) - 1(x - 13) = (x - 13)(x - 1) 

(iv) 9z² - x² - 4y² + 4xy = 9z² - (x - 2y)² = (3z - x + 2y)(3z + x - 2y) 

(v) abc - ab - c + 1 = ab(c - 1) - (c - 1) = (ab - 1)(c - 1)