Question

Factorise

27y³ - 343x³

Answer 1

Factoring: x³-y³

Theory : A difference of two perfect cubes, a³ - b³ can be factored into
(a-b) • (a² +ab +b²)

Proof : (a-b)•(a²+ab+b²) =
a³+a²b+ab²-ba²-b²a-b³ =
a³+(a²b-ba²)+(ab²-b²a)-b³ =
a³+0+0+b³ =
a³+b³

Check : x³ is the cube of x¹

Check : y³ is the cube of y¹

Factorization is :
(x - y) • (x² + xy + y²)

Similarly this question can be written in the format (3y)^3-(7y)^3...
thus it become perfect sqaure