Question

factorise :
a³-49a(x-2y)²​

Answer 1

Given : a³ - 49a(x-2y)²

To find : Factors

Identity used :

$\sf \bullet \: {x}^{2} - {y}^{2} = (x+y)(x-y) \\ \sf \bull \: {x}^{m} \times {y}^{m} \: = \: {xy}^{m}$

• a(x+y) = ax + ay

Solution :

a³ - 49a(x-2y)²

Take 'a' as common

= a{ a² - 49(x-2y)² }

= a{ a² - (7²)×(x-2y)² }

= a{ a² - (7×(x-2y) )² }

= a[ {a +7(x-2y) } { a - 7(x-2y) }

= a × (a + 7x - 14y) × (a -7x + 14y)

ANSWER :

Factors are

• a
• (a + 7x - 14y)
• (a -7x + 14y)

Other identity :

• (a+b)² = (a²+b²+2ab)
• (a-b)² = (a²+b²-2ab)