Factories the following

(p² – 2pq + q²) – r²

In the given expression p² – 2pq + q²

1^st and last terms are perfect square

⇒ p² = p × p

⇒ q² = q × q

And the middle expression is in form of 2ab

2pq = 2 × p × q

∴ p × p - 2 × p × q + q × q

Gives (a-b)² = a²-2ab + b²

⇒ In p² – 2pq + q²

a = p and b = q;

∴ p² – 2pq + q² = (p-q)²

Now the given expression is (p-q)²– r²

Both terms are perfect square

⇒ (p-q)² = (p-q) × (p-q)

⇒ r² = r × r

∴ (p-q)²– r² Seems to be in identity a²-b² = (a + b)(a-b)

Where a = (p-q) and b = r;

(p-q)²– r² = (p-q-r) (p-q + r)

Hence the factors of (p² – 2pq + q²) – r² are (p-q-r) and (p-q + r)