Evaluate 4.2 × 4.2 − 1.9 × 1.9 and verify it equals 2.3 × 6.1.

Problem restatementCompute the value of 4.2² − 1.9². Show it equals the product 2.3 × 6.1.

Concept/ApproachUse the identity a² − b² = (a − b)(a + b) with a = 4.2 and b = 1.9.

Step-by-step calculation4.2² − 1.9² = (4.2 − 1.9)(4.2 + 1.9)= 2.3 × 6.1= 14.03

Verification/AlternativeDirect squares: 4.2² = 17.64; 1.9² = 3.61; difference = 14.03, matching 2.3 × 6.1.

Common pitfallsForgetting the difference-of-squares identity and doing unnecessary long multiplication.

Final Answer14.03