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Algebraic Identities

Question 33Th...

Question

Question 33

The value of $(a + b)^{2} - (a - b)^{2}$ is
a) $4 a b$
b) $- 4 a b$
c) $2 a^{2} + 2 b^{2}$
d) $2 a^{2} - 2 b^{2}$

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Solution

We have,
$(a + b)^{2} - (a - b)^{2} = a^{2} + b^{2} + 2 a b - (a^{2} + b^{2} - 2 a b) [∵ (a + b)^{2} = a^{2} + b^{2} + 2 a b a n d (a - b)^{2} = a^{2} + b^{2} - 2 a b] = a^{2} + b^{2} + 2 a b - a^{2} - b^{2} + 2 a b = a^{2} + b^{2} - b^{2} - a^{2} + 2 a b + 2 a b = 4 a b$
[combining the like terms]

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Similar questions

Q. Question 32

The value of

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

2 a + 2 b

2 a - 2 b

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

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

The maximum value of the expression $y = 2 (a - x) (x + \sqrt{x^{2} + b^{2}})$ is

Question 58 (f)

Subtract:

$- 2 a^{2} - 2 b^{2}$ from $- a^{2} - b^{2} + 2 a b .$

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

.

a \neq b

2 a^{2} = 7 a - 5

2 b^{2} = 7 b - 5

then find the value of

a^{2} + b^{2}

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Algebraic Identities

Standard VIII Mathematics

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