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Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
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Simplify the following expression: 1.684.32×4.32−2.64×2.64
6.94
6.56
6.99
6.96
6.96
Use the algebraic identity a2−b2=(a−b)(a+b) where a=4.32 and b=2.64. Notice that 4.32−2.64=1.68, which directly cancels out with the denominator.
Expression:1.684.32×4.32−2.64×2.64
a2−b2=(a−b)(a+b)
Use the algebraic identity a2−b2=(a−b)(a+b) where a=4.32 and b=2.64. Notice that 4.32−2.64=1.68, which directly cancels out with the denominator.
Multiplying decimals manually (4.32×4.32 and 2.64×2.64), which takes too long and leads to arithmetic errors under exam time pressure.
Identify the algebraic form
Observe the numerator which is in the form of a2−b2, where a=4.32 and b=2.64.
4.32×4.32−2.64×2.64=(4.32)2−(2.64)2
Apply the difference of squares identity
Using the identity a2−b2=(a−b)(a+b), expand the numerator.
(4.32−2.64)(4.32+2.64)
Calculate the difference
Subtract 2.64 from 4.32 to find the first factor.
4.32−2.64=1.68
Substitute back and simplify
Substitute 1.68 into the expression and cancel out the common term with the denominator.
1.681.68×(4.32+2.64)=4.32+2.64
Final addition
Add the two numbers to get the final simplified result.
4.32+2.64=6.96
D is correct because applying the difference of squares identity simplifies the fraction to 4.32+2.64=6.96.
Recognizing standard algebraic forms in arithmetic calculations saves considerable time in quantitative aptitude and simplification problems across competitive exams.
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