Question

1) 3 (x - y)² - 10 (x-y) + 8​

Answer 1

`(3x-3y-4)(x-y-2)`

Explanation:

Given expression:

`3(x-y)^2-10(x-y)+8`

Let u = (x - y):

`\implies 3u^2-10u+8`

To factor a quadratic in the form
`ax^2+bx+c` find two numbers that multiply to
`ac` and sum to
`b`:

`\implies ac=3 \cdot 8=24`

`\implies b=-10`

Therefore, the numbers are: -6 and -4.

Rewrite
`b` as the sum of these two numbers:

`\implies 3u^2-6u-4u+8`

Factor the first two terms and the last two terms separately:

`\implies 3u(u-2)-4(u-2)`

Factor out the common term (u - 2):

`\implies (3u-4)(u-2)`

Substitute back in u = (x - y):

`\implies (3(x-y)-4)((x-y)-2)`

Simplify:

`\implies (3x-3y-4)(x-y-2)`