Question

In the expansion of (2x² - 8) (x - 4)²; find the value of coefficient of x³.

Answer 1

( 2x² - 8 )( x - 4 )²
= ( 2x² - 8 )( x² - 8x + 16 )

= 2x²( x² - 8x + 16 ) - 8( x² - 8x + 16 )
= 2x⁴ - 16x³ + 32x² - 8x² + 64x -128
= 2x⁴ - 16x³ + 24x² + 64x - 128
Hence,
Coefficient of x³ = - 16