The correct option is B a^3 b^3+2a^2b 2ab^2+ab^2 ba^2(a b)× (a^2 + 2ab + b^2) = (a× a^2 +a× 2ab + a× b^2) +(( b)× a^2+ ( b)× 2ab + ( b)× b^2 =a^3+2a^2b+ab^2 b ...

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Long Division

a-b ×a2+2 a b...

Question

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

a^{3} - b^{3} + a b^{2} - b a^{2}

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a^{3} - b^{3} + 2 a^{2} b - 2 a b^{2} + a b^{2} - b a^{2}

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2 a^{2} b + 2 a b^{2}

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a^{3} + b^{3} + 2 a^{2} b + 2 a b^{2} + a b^{2} + b a^{2}

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Solution

The correct option is B $a^{3} - b^{3} + 2 a^{2} b - 2 a b^{2} + a b^{2} - b a^{2}$
$(a - b) \times (a^{2} + 2 a b + b^{2})$
$= (a \times a^{2} + a \times 2 a b + a \times b^{2}) + ((- b) \times a^{2} + (- b) \times 2 a b + (- b) \times b^{2} = a^{3} + 2 a^{2} b + a b^{2} - b a^{2} - 2 a b^{2} - b^{3} = a^{3} - b^{3} + 2 a^{2} b - 2 a b^{2} + a b^{2} - b a^{2}$

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Similar questions

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

Find:
$(a + b + c) \times (a + b - c) =$

Simplify $\frac{a - b}{a} + \frac{a + b}{b}$

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}

Q. More than One Answer Type
एक से अधिक उत्तर प्रकार के प्रश्न

If a – b = a² + b² + 2ab and a + b = a² + b² – 2ab, then which of the following is/are correct?

यदि a – b = a² + b² + 2ab तथा a + b = a² + b² – 2ab, तब निम्नलिखित में से कौनसा/कौनसे विकल्प सही है/हैं?

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(a−b)×(a2+2ab+b2) = ______

The correct option is B a3−b3+2a2b−2ab2+ab2−ba2(a−b)×(a2+2ab+b2) =(a×a2+a×2ab+a×b2)+((−b)×a2+(−b)×2ab+(−b)×b2=a3+2a2b+ab2−ba2−2ab2−b3=a3−b3+2a2b−2ab2+ab2−ba2

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