Join 60,000+ competitive exam aspirants
or with email
Your Cart
SubtotalтВ╣0
TotalтВ╣0
Examoogle тАв User тАв info@examoogle.com тАв EE-2024-8821
Chapter 1 of 12 тАв Page 1 of 248ЁЯФТ Protected PDF тАв Watermarked
Join 60,000+ competitive exam aspirants
Write the expanded form of (7a + 9b + 4c) 2 .
49a 2 + 81b 2 + 16c 2 + 126ab + 72bc + 56ac
49a 2 + 81b 2 + 16c 2 + 126ab + 72bc + 66ac
49a 2 + 81b 2 + 16c 2 + 130ab + 72bc + 56ac
49a 2 + 81b 2 + 16c 2 + 126ab + 67bc + 56ac
49a 2 + 81b 2 + 16c 2 + 126ab + 72bc + 56ac
The expression (7a + 9b + 4c)2 follows the algebraic identity (x + y + z)2 = x┬▓ + y┬▓ + z┬▓ + 2xy + 2yz + 2zx. Substituting x=7a, y=9b, and z=4c, we calculate (7a)2 + (9b)2 + (4c)2 + 2(7a)(9b) + 2(9b)(4c) + 2(4c)(7a), resulting in 49a┬▓ + 81b┬▓ + 16c┬▓ + 126ab + 72bc + 56ac.
The expression (7a + 9b + 4c)2 follows the algebraic identity (x + y + z)2 = x┬▓ + y┬▓ + z┬▓ + 2xy + 2yz + 2zx. Substituting x=7a, y=9b, and z=4c, we calculate (7a)2 + (9b)2 + (4c)2 + 2(7a)(9b) + 2(9b)(4c) + 2(4c)(7a), resulting in 49a┬▓ + 81b┬▓ + 16c┬▓ + 126ab + 72bc + 56ac.
This mathematical identity is a foundational concept in Algebra, a branch of Mathematics often tested in competitive exams like SSC CGL and RRB under the 'Quantitative Aptitude' section, linked to the general logic required for systematic data analysis.
The square of a trinomial includes the sum of squares of each term and twice the sum of product pairs.
Identity: (a + b + c)2 = a┬▓ + b┬▓ + c┬▓ + 2ab + 2bc + 2ca.
Order of terms does not change the result due to the commutative property of addition.
Calculation verification: 2 * 7 * 9 = 126 (ab term), 2 * 9 * 4 = 72 (bc term), 2 * 4 * 7 = 56 (ac term).
Option B is incorrect because it contains 66ac instead of 56ac.
Option C is incorrect because 130ab is mathematically inconsistent with 279.
Option D is incorrect because 67bc is mathematically inconsistent with 294.
A is correct тАФ the expansion follows the trinomial square identity resulting in 49a┬▓ + 81b┬▓ + 16c┬▓ + 126ab + 72bc + 56ac.
Algebraic identities are frequently used in simplifying complex expressions within 'Data Interpretation' and 'Arithmetic Geometry' questions in competitive exams.
Get instant step-by-step AI explanations, full shift Previous Year Papers (SSC GD, RRB, SSC JE), and regional rank analysis on the official Examoogle App.
Free Download тАв 100K+ Aspirants