Find the constant term.

01 / Standard#Your turn

\left(2\sqrt x-\frac1{\sqrt x}\right)^6

Official paper · jm01-2023 · I.6 · PDF 2

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Track the exponent when choosing k inverse-root factors.

Hint 2

The exponent must be zero.

Worked solution

C: −160.

Checks and common pitfalls: The odd number of negative factors makes the term negative.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Write the general term.
$\binom6k2^{6-k}(-1)^kx^{3-k}$
Choose k=3 and evaluate.
$\binom632^3(-1)^3=-160$

Think first. Reveal a hint when the class is ready.

2023 JM01