Question

factorise 5roota^3-2root2b^3​

Answer 1

Answer:

Let us split the terms

5 √5x³ -81 √3 y³

5 can be written as √5.√5, and we split 81 into 3 and √3 such that we can form cubes

√5.√5.√5.x³ - 3.3.3.√3.√3.√3 y³

we can arrange it as

(√5x).(√5x).(√5x) -( 3√3y). (3√3y). (3√3y)

= (√5x)³-(3√3y)³

which can be factorised using the formula a³-b³

=(a-b)(a²+ab+b²)

=(√5x-3√3y) ((√5x)²+(√5x.3√3y) +(3√3y)²)

=(√5x-3√3y) {5x² +3√15 xy +9.3 y²)

=(√5x-3√3y) {5x² +3√15 xy +27 y²)

As we cannot simplify further, this will be the final factorised form