Question

Evaluate cubes using suitable identites:
1) 997cube
2)(4a-2b-3c)^2

Answer 1

Hey friend,

(1)997³

=(1000-3)³

(a-b)³=a³-b³-3ab(a-b)

(1000-3)³ = 1000³ - 3³ - 3(1000)(1) [1000-3]

=1000000000 - 27 -3000(997)

=1000000000 - 27 - 2991000

=997008973

(2) (4a-2b-3c)²

=(4a+(-2b)+(-3c)²

(a+b+c)² = a²+b²+c²+2(ab+bc+ca)

=(4a)²+(-2b)²+(-3c)² + 2[(4a)(-2b) + (-2b)(-3c) + (-3c)(4a)]

=16a²+4b²+9c²+2(-8ab+6bc-12ac)

Hope it helps