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Simplify the following expression: 9994×10006
99999976
99999924
99999964
91999924
99999964
Use the algebraic identity (a−b)(a+b)=a2−b2. Here, let a=10000, b=6. Then (10000−6)(10000+6)=100002−62=100000000−36=99999964.
Multiplication expression: 9994 × 10006
(a−b)(a+b)=a2−b2
Use the algebraic identity (a−b)(a+b)=a2−b2. Here, let a=10000, b=6. Then (10000−6)(10000+6)=100002−62=100000000−36=99999964.
Students often multiply longhand manually, which is slow and prone to carrying errors. Applying the difference of squares identity makes the calculation simple and accurate.
Identify the numbers
Observe that both numbers are equidistant from a round number, 10000. Write the numbers as (10000−6) and (10000+6).
9994=10000−6 and 10006=10000+6
Apply Identity
Use the difference of squares identity (a−b)(a+b)=a2−b2 where a=10000 and b=6.
(10000−6)(10000+6)=100002−62
Calculate and Simplify
Square 10000 to get 100,000,000 and square 6 to get 36. Subtract 36 from 100,000,000.
100000000−36=99999964
C is correct because 9994 × 10006 = (10000 - 6)(10000 + 6) = 100,000,000 - 36 = 99,999,964.
This identity is fundamental for mental math in competitive exams, especially when dealing with squares and products of numbers near powers of 10 (e.g., 99², 102 × 98).
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