Perform the following divisions and give the remainders.
$(a^{2} + 2 a b + b^{2}) \div (a + b)$

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Solution

According to question,

$\frac{(a^{2} + 2 a b + b^{2})}{a + b}$

$⟹ \frac{(a + b)^{2}}{a + b}$

$⟹ a + b$

Here, Numerator is completely divisible by denominator.

Hence, remainder is $0$ .

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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) $(a + b)^{2} = a^{2} + 2 a b - b^{2}$

Q. Question 3

Which of the following is correct?
a)

(a - b)^{2} = a^{2} + 2 a b - b^{2}

(a - b)^{2} = a^{2} - 2 a b + b^{2}

(a - b)^{2} = a^{2} - b^{2}

(a + b)^{2} = a^{2} + 2 a b - b^{2}

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Perform the following divisions and give the remainders.(a2+2ab+b2)÷(a+b)

According to question,(a2+2ab+b2)a+b⟹(a+b)2a+b⟹a+bHere, Numerator is completely divisible by denominator.Hence, remainder is 0.

Perform the following divisions and give the remainders.
$(a^{2} + 2 a b + b^{2}) \div (a + b)$

According to question,

$\frac{(a^{2} + 2 a b + b^{2})}{a + b}$

$⟹ \frac{(a + b)^{2}}{a + b}$

$⟹ a + b$

Here, Numerator is completely divisible by denominator.

Hence, remainder is $0$ .