Factorize the expressions and divide them as directed:

26z³(32z²–18) ÷ 13z²(4z – 3)

In the given term

Dividend = 26z³(32z²–18)

Take out the common factor in binomial term

⇒ 2 × 13 × z × z × z (2 × 2 × 2 × 2 × 2 × z × z – 2 × 3 × 3)

⇒ 2 × 2 × 13 × z × z × z (2 × 2 × 2 × 2 × z × z – 3 × 3)

⇒ 52z³(16z² – 9)

In given expression (16z² – 9)

Both terms are perfect square

⇒ 16z² = 4z × 4z

⇒ 9 = 3 × 3

∴ (16z² – 9) Seems to be in identity a²-b² = (a + b)(a-b)

Where a = 4z and b = 3;

(16z² – 9) = (4z + 3)(4z – 3)

Hence the factors of (16z² – 9)are (4z + 3) and (4z – 3)

Divisor = 13z²(4z – 3)

=

=

= 4z(4z + 3)

Hence dividing 26z³(32z²–18) by 13z²(4z – 3) gives out 4z(4z + 3)