Question

resolve into factors
15x^2-24y^2-6z^2+2xy-xz+24yz​

Answer 1

1. First deal with the terms that in x or y or both.
2. 15x²-24y²+2xy are the terms in x and y.
3. On factorising, we can split 2xy as 20xy-18xy.
4. 15x²+20xy-18xy-24y².
5. We get the equation after factorization as (3x+4y)(5x−6y).
6. Entire equation becomes (3x+4y)(5x−6y)−6z²−xz+24yz.
7. 3x+4y and 5x-6y are already present in equation. Using them as factors we can simplify rest of the equation.
8. Solving latter part, equation becomes,

              (3x+4y)(5x−6y)+3z(3x+4y)−2z(5x−6y)

    8. On simplifying and taking common terms,

    15x²-24y²-6z²+2xy-xz+24yzz= (3x+4y−2z)(5x−6y+3z).