Question

How do you factor `8x^2-10xy+3y^2`?

Answer 1

Factor: `f(x, y) = 8x^2 - 10xy + 3y^2`

Ans: (2x - y)(4x - 3y)

Explanation:

Find 2 numbers p and q, knowing (pq) = 24 and (p + q) = -10. They are -4 and -6. Replace the term -10xy by the 2 terms -4xy and - 6xy.
`f(x, y) = 8x^2 - 4xy - 6xy + 3y^2.`
f(x, y) = 4x(2x - y) - 3y(2x - y)
f(x. y) = (2x - y)(4x - 3y)
Check by developing:
`8x^2 - 6xy - 4xy + 3y^2 = 8x^2 - 10xy + 3y^2.` OK