What is the 4th term of the given expansion?

Correct answer: d − 160 x³

n = 3, the 4th term of (1 − 2x)⁶ is ⁶C₃(−2x)³ = 20 × (−8x³) = −160x³, so this is the value.

Why the other options are wrong

• a 160 x²: 160x² has the wrong power and sign; the 4th term has x³. The right answer is − 160 x³.
• b 60 x³: 60x³ has the wrong number and sign; ⁶C₃ = 20 and (−2)³ = −8. The right answer is − 160 x³.
• c − 60 x³: −60x³ has the wrong number; 20 × 8 = 160. The right answer is − 160 x³.