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Write the expanded form of (9a + 4b + 5c) 2 .
81a 2 + 16b 2 + 25c 2 + 72ab + 35bc + 90ac
81a 2 + 16b 2 + 25c 2 + 72ab + 40bc + 100ac
81a 2 + 16b 2 + 25c 2 + 72ab + 40bc + 90ac
81a 2 + 16b 2 + 25c 2 + 76ab + 40bc + 90ac
81a 2 + 16b 2 + 25c 2 + 72ab + 40bc + 90ac
The expansion of a trinomial squared is given by the algebraic identity (x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx. Substituting x = 9a, y = 4b, and z = 5c yields (9a)² + (4b)² + (5c)² + 2(9a)(4b) + 2(4b)(5c) + 2(9a)(5c) = 81a² + 16b² + 25c² + 72ab + 40bc + 90ac.
The expansion of a trinomial squared is given by the algebraic identity (x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx. Substituting x = 9a, y = 4b, and z = 5c yields (9a)² + (4b)² + (5c)² + 2(9a)(4b) + 2(4b)(5c) + 2(9a)(5c) = 81a² + 16b² + 25c² + 72ab + 40bc + 90ac.
Algebraic identities represent foundational mathematical principles widely tested under the Quantitative Aptitude and General Awareness numerical sections of Indian competitive examinations like SSC, RRB, and State PSCs.
Standard identity used: (x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx.
First term squared: (9a)² = 81a².
Second term squared: (4b)² = 16b².
Third term squared: (5c)² = 25c².
Cross-product terms: 2(9a)(4b) = 72ab, 2(4b)(5c) = 40bc, 2(9a)(5c) = 90ac.
Option A has an incorrect product term for 2bc: 35bc instead of 40bc.
Option B has an incorrect product term for 2ac: 100ac instead of 90ac.
Option D has an incorrect product term for 2ab: 76ab instead of 72ab.
C is correct — Applying the identity (x + y + z)² gives 81a² + 16b² + 25c² + 72ab + 40bc + 90ac.
Questions based on standard algebraic expansions like (a + b)³, (a - b)³, and (a + b + c)² are frequently asked in quantitative and general mental ability sections of SSC CGL, CHSL, and Railway exams.
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