Join 60,000+ competitive exam aspirants
or with email
Your Cart
Subtotal₹0
Total₹0
Examoogle • User • info@examoogle.com • EE-2024-8821
Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
Join 60,000+ competitive exam aspirants
Simplify the following expression: 1.684.35×4.35−2.67×2.67
7.02
7.04
6.99
6.96
7.02
Recognize the numerator as the difference of two squares a2−b2=(a−b)(a+b). Here a=4.35 and b=2.67. Note that a−b=4.35−2.67=1.68, which cancels out the denominator.
Expression to simplify: (4.35 * 4.35 - 2.67 * 2.67) / 1.68
a2−b2=(a−b)(a+b)
Recognize the numerator as the difference of two squares a2−b2=(a−b)(a+b). Here a=4.35 and b=2.67. Note that a−b=4.35−2.67=1.68, which cancels out the denominator.
Multiplying the decimals manually is time-consuming and prone to calculation errors; always check for algebraic identities first.
Identify algebraic form
Observe that the numerator 4.35×4.35−2.67×2.67 is in the form a2−b2 where a=4.35 and b=2.67.
a2−b2=(a−b)(a+b)
Apply the identity
Substitute the values into the algebraic identity (4.35−2.67)(4.35+2.67).
(4.35−2.67)(4.35+2.67)=1.68×7.02
Simplify the fraction
Substitute the simplified numerator back into the original expression: 1.681.68×7.02. The factor 1.68 cancels out.
1.681.68×7.02=7.02
A is correct because the expression simplifies to 4.35+2.67=7.02 after canceling the difference term.
This identity-based simplification is frequently tested in RRB and SSC exams to test mental calculation speed over brute-force arithmetic.
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 • 100K+ Aspirants