Question

Factorise : 3x3 – 45x2y + 225xy2 – 375y3​

Answer 1

Answer:

$3(x - 5y)^{3}$

Step-by-step explanation:

$3x^{3} - 45x^{2} y + 225xy^{2} - 375y^{3} \\=3(x^{3} - 15x^{2} y + 75xy^{2} - 125y^{3})\\ = 3[x^{3} - (5y)^{3} - 15xy(x - 5y)]\\= 3(x - 5y)[(x^{2} + x.5y + (5y)^{2} ) - 15xy]\\= 3(x - 5y)[(x^{2} - 2.x.5y + (5y)^{2} ]\\= 3(x - 5y)[(x - 5y)^{2} ]\\= 3(x - 5y)^{3}$