Question

Expand the following:

(2p + 3)(2p – 4)(2p – 5)

Answer 1

(2p + 3)(2p – 4)(2p – 5)

(x + a)(x + b)(x + c) ≡ x³ + (a + b + c) x² + (ab + ba + ca) x + abc

(2p + 3)(2p – 4)(2p – 5) = (2p)³ + (3 – 4 – 5) (2p)² + [(3 × – 4)² + (– 4 × – 5) + (– 5 × 3)] 2p + 3 × – 4 × – 5

= 8p³ + (– 6) (4p²) + [–12 + 20 + (–15)] 2p + 60

= 8p³ – 24p² + (–7)2p + 60

(2p + 3)(2p – 4)(2p – 5) = 8p³ – 24p² – 14p + 60