Question

Factorise the following polynomials using a² - b² = ( a + b) ( a - b).

a) 12 - 27x²

b) x² / 4a² - y² / 9b²


$c) (\: 3 \ \frac{1}{2} {}) {}^{2} - \: (1 \ \frac{1}{2} ) {}^{2}$
d) ( 0.7)² - ( 0.4)²

e) a³ - 144a

f) 1 - 81 ( 7a + 3b)²

g) 121 ( 35 - 7t)² - 225 ( 18 - 3t)² ​

Answer 1

Step-by-step explanation:

a) 12 - 27x² =3(4-9x²) now u can solve

b) x² / 4a² - y² / 9b² = (x/2a + y/3b) (x/2a - y/3b)

c) is not readable

d) ( 0.7)² - ( 0.4)² = (0.7+0.4)(0.7-0.4)

e) a³ - 144a =a( a^2-144) = a(a+12)(a-12)

f) 1 - 81 ( 7a + 3b)² = 1 - [ 9²(7a+3b)²]

= 1² - [9(7a+3b)]² = 1²-(63a+27b)² = (1 + 63a+27b)(1 - 63a - 27b)

g) 121 ( 35 - 7t)² - 225 ( 18 - 3t)²

= similar to (f) Here 121= 11² and 225 = 15²