Factorize the expressions and divide them as directed:

15lm (2p²–2q²) ÷ 3l (p + q)

In the given term

Dividend = 15lm (2p²–2q²)

In given expression (2p²–2q²)

Take out the common factor in binomial term

⇒ (2 × p × p – 2 × q × q)

→ 2(p² – q²)

Both terms are perfect square

⇒ p² = p × p

⇒ q² = q × q

∴ (p² – q²) Seems to be in identity a²-b² = (a + b)(a-b)

Where a = p and b = q;

p² – q² = (p + q)(p – q)

Hence the factors of p² – q² are (p + q) and (p – q)

Divisor = 3l (p + q)

=

=

= 10m(p – q)

Hence dividing 15lm (2p²–2q²) by 3l (p + q) gives out 10m(p – q)