SSC CGL 2024 Tier-I · 25 September 2024, Shift 2 · Quantitative Aptitude · Question 21 of 99

Text as printed on a candidate's response sheet for this shift; answer per SSC's tentative key as marked on that sheet. Solution last reviewed 10 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. The questions and options here are reproduced as printed on a candidate's own response sheet for this shift — the Commission's text, unchanged. Each answer is SSC's tentative key as marked on that sheet; SSC allowed challenges to it and never publishes a final key. The solutions are written by UnlockIAS.

The value of (x + y)² + (x − y)² is equal to:

Answer

Why

Correct — D. The stem and all four options are images. The stem asks for the value of (x + y)² + (x − y)², and option (d) shows 2(x² + y²).

(x + y)² = x² + 2xy + y²
(x − y)² = x² − 2xy + y²
Add the two: the +2xy and −2xy cancel

Sum = 2x² + 2y² = 2(x² + y²) → option (d)

Why the others are wrong

(a)
Option (a) shows 4xy, which is (x + y)² − (x − y)². Subtracting keeps the cross term and cancels the squares — the exact opposite of what adding does.
(b)
Option (b) shows (2x + 2y)² = 4x² + 8xy + 4y². The surviving 8xy settles it: the true sum has no xy term at all.
(c)
Option (c) shows 2(x + y)² = 2x² + 4xy + 2y². That treats (x − y)² as equal to (x + y)², which is only true when xy = 0.

Concept

Two identities do all the work here, and they are worth holding as a pair.

(a + b)² + (a − b)² = 2(a² + b²)
(a + b)² − (a − b)² = 4ab

Adding cancels the cross term; subtracting cancels the squares. Every option printed here is one of those two results or a mis-square of them, so recognising the pair settles the item without expanding anything.

Substituting x = 2 and y = 1 separates all four options in seconds: they come to 8, 36, 18 and 10, while the expression itself is 3² + 1² = 10.

Key facts

(a + b)² + (a − b)² = 2(a² + b²), because the 2ab terms cancel.
(a + b)² − (a − b)² = 4ab, because the squares cancel instead.
At x = 2 and y = 1 the expression is 3² + 1² = 10, matching 2(4 + 1).

Study next

The paired identities (a + b)² and (a − b)², and what adding or subtracting them leavesSubstituting small values to eliminate algebraic options under time pressureWriting a² + b² in terms of (a + b) and ab

Common traps

Answering 4xy, which is the difference of the two squares rather than their sum
Adding what is inside the brackets first and then squaring
Confusing the option images 2(x + y)² and 2(x² + y²), where the squares sit in different places

Both the stem and every option arrive as pictures, so the item turns on reading where each square sits before any algebra begins.

Related PYQs

No directly related past PYQ was found.