44³ + 35³−53³ + 159 is equal to:

Correct — A.
Test the shortcut first: 44 + 35 = 79, not 53, so the a + b = c identity does not apply. Cube each term.

44³ = 1936 × 44 = 85184
35³ = 1225 × 35 = 42875
53³ = 2809 × 53 = 148877

Add the first two: 85184 + 42875 = 128059
Subtract 53³: 128059 − 148877 = −20818
Add 159: −20818 + 159 = −20659 → option (a)

Why the others are wrong

• (b)
  0 — 0 would need the cubes to cancel, but 53³ = 148877 is larger than 44³ + 35³ = 128059 by 20818. Adding 159 cannot close that gap.
• (c)
  −18659 — −18659 is exactly 2000 above the true total. It shares its last three digits with −20659, so a units-digit check cannot separate them. The full cube arithmetic does.
• (d)
  1 — 1 would need the expression to collapse almost to nothing, but 53³ outweighs 44³ + 35³ by 20818, and adding 159 still leaves −20659.

Cube-sum questions have two routes. First test for the identity: if a + b = c, then a³ + b³ − c³ = −3abc, and the cubes reduce to one product.

Here 44 + 35 = 79, not 53, so no identity helps and the job is plain arithmetic.

Cube through the square (44² = 1936, then × 44) and keep the signs apart: add the two positive cubes, then subtract the negative one.

Key facts

• If a + b = c, then a³ + b³ − c³ = −3abc.
• If a + b + c = 0, then a³ + b³ + c³ = 3abc.
• 44³ = 85184, 35³ = 42875 and 53³ = 148877.

Common traps

• Assuming the identity applies because the stem looks like a³ + b³ − c³, without checking whether 44 + 35 equals 53
• Settling for an option that merely looks close: −18659 sits 2000 from −20659 with the same last three digits, so a slip of 2000 in one cube lands on it

No directly related past PYQ was found.