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Question

Simplify the following using the formula: (a−b)(a+b)=a2−b2: (i) (82)2−(18)2 (ii) (467)2−(33)2 (iii) (79)2−(69)2 (iv) 197×203 (v) 113×87 (vi) 95×105 (vii) 1.8×2.2 (viii) 9.8×10.2

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Solution

(i) (82)2−(18)2=(82+18)(82−18){(a+b)(a−b)=a2−b2}=100×64=6400(ii) (467)2−(33)2=(467+33)(467−33)=500×434=217000(iii) (79)2−(69)2=(79+69)(79−69)=148×10=1480(iv) 197×203=(200−3)(200+3)=(200)2−(3)2=40000−9=39991(v) 113×87=(100+13)(100−13)=(100)2−(13)2=10000−169=9831(vi) 95×105=(100−5)(100+5)=(100)2−(5)2=10000−25=9975(vii) 1.8×2.2=(2.0−0.2)(2.0+0.2)=(2.0)2−(0.2)2=4.00−0.04=3.96(viii) 9.8×10.2=(10.0−0.2)(10.0+0.2)(10.0)2−(0.2)2=100.00−0.04=99.96

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The text contains a series of mathematical questions that involve simplifying expressions using the difference of squares formula, followed by detailed solutions for each question.
multiple_questions_with_answers
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
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You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Simplify the following using the formula: (a−b)(a+b)=a2−b2: (i) (82)2−(18)2 (ii) (467)2−(33)2 (iii) (79)2−(69)2 (iv) 197×203 (v) 113×87 (vi) 95×105 (vii) 1.8×2.2 (viii) 9.8×10.2

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Solution

(i) (82)2−(18)2=(82+18)(82−18){(a+b)(a−b)=a2−b2}=100×64=6400(ii) (467)2−(33)2=(467+33)(467−33)=500×434=217000(iii) (79)2−(69)2=(79+69)(79−69)=148×10=1480(iv) 197×203=(200−3)(200+3)=(200)2−(3)2=40000−9=39991(v) 113×87=(100+13)(100−13)=(100)2−(13)2=10000−169=9831(vi) 95×105=(100−5)(100+5)=(100)2−(5)2=10000−25=9975(vii) 1.8×2.2=(2.0−0.2)(2.0+0.2)=(2.0)2−(0.2)2=4.00−0.04=3.96(viii) 9.8×10.2=(10.0−0.2)(10.0+0.2)(10.0)2−(0.2)2=100.00−0.04=99.96

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The text contains a series of mathematical questions that involve simplifying expressions using the difference of squares formula, followed by detailed solutions for each question.

TYPE: MULTIPLE_QUESTIONS_WITH_ANSWERS