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What is the value of (12² - 8²) / 4?
10
20
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20
Use the identity a2−b2=(a−b)(a+b). Here, (12−8)(12+8)=4×20. Dividing by 4 leaves 20.
Expression to evaluate is (12² - 8²) / 4.
a2−b2=(a−b)(a+b)
Use the identity a2−b2=(a−b)(a+b). Here, (12−8)(12+8)=4×20. Dividing by 4 leaves 20.
Students often spend time calculating 122=144 and 82=64 separately (which is fine) but fail to perform the final division by 4 correctly.
Apply Difference of Squares Identity
Identify the numerator as a difference of two squares where a=12 and b=8.
122−82=(12−8)(12+8)
Simplify the Expression
Perform the arithmetic within the parentheses.
(4)(20)
Divide by the Denominator
Divide the result by the denominator 4 provided in the original expression.
44×20=20
B is correct because the expression simplifies to 480, which equals 20.
Recognizing patterns like a2−b2 is crucial for RRB exams to avoid long multiplications, as it also appears in square root estimation and number series problems.
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