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

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

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4 a b

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2 a^{2}

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2 b^{2}

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Solution

The correct option is B $4 a b$
Using the identities,

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

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

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Similar questions

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}}}

Q. Factorise:

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

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(a+b)2−(a−b)2=_______

The correct option is B 4abUsing the identities, (a+b)2=a2+2ab+b2 (a−b)2=a2−2ab+b2 So, (a+b)2−(a−b)2 =(a2+2ab+b2)−(a2−2ab+b2) ​​​​​​​=4ab

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

The correct option is B $4 a b$
Using the identities,

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

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