Question

Factorise 54x^3+10 sqrt 5 y^3+18 sqrt 5x^2 y+30xy^2

Answer 1

Answer:

$\bold{54 {x}^{3} + 10 \sqrt{5} {y}^{3} + 18 \sqrt{5} {x}^{2} y + 30x {y}^{2} }\\ \\ = \bold{2(3x + \sqrt{5}y)(9 {x}^{2} + 5 {y}^{2} )}$

Step-by-step explanation:

$54 {x}^{3} + 10 \sqrt{5} {y}^{3} + 18 \sqrt{5} {x}^{2} y + 30x {y}^{2}$

To factorise the polynomial shuffle the terms so that we can take common terms from the first two and last two terms,as shown below

$= (54 {x}^{3} + 10 \sqrt{5} {y}^{3} + 18 \sqrt{5} {x}^{2} y + 30x {y}^{2}) \\ \\ = 54 {x}^{3} + 18 \sqrt{5} {x}^{2}y + 30x {y}^{2} + 10 \sqrt{5} {y}^{3} \\ \\ = 18 {x}^{2} (3x + \sqrt{5}y) + 10 {y}^{2}(3x + \sqrt{5}y) \\ \\ = (3x + \sqrt{5}y)(18 {x}^{2} + 10 {y}^{2} ) \\ \\ = (3x + \sqrt{5}y).2.(9 {x}^{2} + 5 {y}^{2} ) \\ \\ = \bold{2(3x + \sqrt{5}y)(9 {x}^{2} + 5 {y}^{2} )}$

Hope it helps you.