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Division of a Polynomial by a Polynomial

Question 3Whi...

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Question 3

Which of the following is correct?
a) $(a - b)^{2} = a^{2} + 2 a b - b^{2}$
b) $(a - b)^{2} = a^{2} - 2 a b + b^{2}$
c) $(a - b)^{2} = a^{2} - b^{2}$
d) $(a + b)^{2} = a^{2} + 2 a b - b^{2}$

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Solution

b) $(a - b)^{2} = a^{2} - 2 a b + b^{2}$
$\to$ We have,
$(a - b)^{2} = (a - b) (a - b) = a (a - b) - b (a - b) = a . a - a . b - b . a + b . b = a^{2} - a b - a b + b^{2} = a^{2} - 2 a b + b^{2} [∵ a . b = b . a]$

and $(a + b)^{2} = (a + b) (a + b) = a . a + a . b + b . a + b . b = a^{2} + 2 a b + b^{2}$

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Division of a Polynomial by a Polynomial

Standard VIII Mathematics

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