Question

1) 3 (x - y)² - 10 (x-y) + 8​

Answer 1

Answer:

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

Step-by-step 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:

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