Question

Using algebraic identity, find the coefficients of x², x and constant term without actual expansion

(2x + 3)(2x – 5)(2x – 6)

Answer 1

(2x + 3)(2x – 5)(2x – 6)

∴ Co-efficient of x² = 4 (a + b + c)

= 4(3 + (– 5) + (– 6))

= 4 × (– 8) = – 32

Co-efficient of x = 2 (ab + bc + ca)

= 2[3 × (– 5) + (– 5)(– 6) + (– 6)(3)]

= 2[–15 + 30 – 18] = 2 × (– 3) = – 6

Constant term = abc

= 3 × (– 5) × (– 6)

= 90