Question

factorise 14x^6-45x^3×y^3-14y^6​

Answer 1

Answer:

it is given that, 14x^6 - 45x^3y^3 - 14y^6

= 14x^6 - 49x^3y^3 + 4x^3y^3 - 14y^6

= 7x^3(2x^3 - 7y^3) + 2y^3(2x^3 - 7y^3)

(7x^3 + 2y^3)(2x^3 - 7y^3)

[ it can also be a solution]

now, for (7x³ + 2y³), we can write it (√7x)³ + (√2y)³

from algebraic identity,

a³ + b³ = (a + b)(a² - ab + b³) so, (7x)³ + (√2y)³

= (√7x + √2y)(√49x² +√4y² - 114xy)

similarly from algebraic identity,

a³ - b³ = (a - b)(a² + ab + b²)

or, (2x³ – 7y³) = (√2x)³ − (√7y)³

or, = (√2x - √7y)(√4x² + √49y³ + √14xy)

hence, factorisation of 14x^6 - 45x^3y^3 - 14y^6

=(√7x + 2y) (49x² + √/4y² – 14xy)(2x - 7y)(√4x² + √49y³ + √14xy)