The correct option is D 4abWe know that, (a + b)^2 = a^2 + b^2 + 2ab and nbsp; (a b)^2 = a^2 + b^2 2ab (a + b)^2 (a b)^2 = a^2 + b^2 + 2ab (a^2 + b ...

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Byju's Answer

Standard VIII

Mathematics

Algebraic Identity: (a + b)^2 = a^2 + b^2 + 2ab

a+b2-a-b2=

Question

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

- 4ab

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- 2ab

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

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4ab

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Solution

The correct option is D 4ab
We know that,
$(a + b)^{2} = a^{2} + b^{2} + 2 a b$ and
$(a - b)^{2} = a^{2} + b^{2} - 2 a b$
$(a + b)^{2} - (a - b)^{2} = a^{2} + b^{2} + 2 a b - (a^{2} + b^{2} - 2 a b)$
$= (a^{2} - a^{2}) + (b^{2} - b^{2}) + (2 a b + 2 a b) = 4 a b$

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Similar questions

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

_______

Q. The correct order of stability for the following species is:

B_{2}, B_{2}^{-} a n d B_{2}^{+}

Q. Prove the followings,

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

ii)

(a + b)^{2} - (a - b)^{2} = 4 a b

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. Simplify

\frac{a + \sqrt{a^{2} - b^{2}}}{a - \sqrt{a^{2} - b^{2}}} + \frac{a - \sqrt{a^{2} - b^{2}}}{a + \sqrt{a^{2} - b^{2}}}

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(a+b)2−(a−b)2=_______.

The correct option is D 4abWe know that, (a+b)2=a2+b2+2ab and (a−b)2=a2+b2−2ab (a+b)2−(a−b)2=a2+b2+2ab−(a2+b2−2ab) =(a2−a2)+(b2−b2)+(2ab+2ab)=4ab

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

The correct option is D 4ab
We know that,
$(a + b)^{2} = a^{2} + b^{2} + 2 a b$ and
$(a - b)^{2} = a^{2} + b^{2} - 2 a b$
$(a + b)^{2} - (a - b)^{2} = a^{2} + b^{2} + 2 a b - (a^{2} + b^{2} - 2 a b)$
$= (a^{2} - a^{2}) + (b^{2} - b^{2}) + (2 a b + 2 a b) = 4 a b$