Determine the formula for a^2 b^2The given expression is a^2 b^2.a^2 b^20ex0ex=a^2 ab+ab b^20ex0ex=a(a b)+b(a b)0ex0ex=(a b)(a+b)Hence, a^2 b^2 is equal to (a b ...

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Standard XII

Mathematics

Properties of Determinants

a2-b2 is equa...

Question

$a^{2} - b^{2}$ is equal to

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Solution

Determine the formula for $a^{2} - b^{2}$
The given expression is $a^{2} - b^{2}$ .
$a^{2} - b^{2} = a^{2} - a b + a b - b^{2} = a (a - b) + b (a - b) = (a - b) (a + b)$
Hence, $a^{2} - b^{2}$ is equal to $(a - b) (a + b)$ .

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Similar questions

Q. If

sin θ = \frac{a^{2} - b^{2}}{a^{2} + b^{2}}

then

tan θ

is equal to

Q. Reduced to lowest terms.

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

is equal to

Q. In a triangle ABC,

(a^{2} - b^{2} - c^{2}) tan A + (a^{2} - b^{2} + c^{2}) tan B

is equal to :

Q. If

a + b + c = 0

then

\frac{1}{b^{2} + c^{2} - a^{2}} + \frac{1}{c^{2} + a^{2} - b^{2}} + \frac{1}{a^{2} + b^{2} - c^{2}}

is equal to

Q. Assertion :In any right angled triangle

\frac{a^{2} + b^{2} + c^{2}}{R^{2}}

is always equal to

8

. Reason:

a^{2} = b^{2} + c^{2}

b^{2} = c^{2} + a^{2}

c^{2} = a^{2} + b^{2}

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a2-b2 is equal to

Determine the formula for a2-b2The given expression is a2-b2.a2-b2=a2-ab+ab-b2=aa-b+ba-b=a-ba+bHence, a2-b2 is equal to a-ba+b.

$a^{2} - b^{2}$ is equal to

Determine the formula for $a^{2} - b^{2}$
The given expression is $a^{2} - b^{2}$ .
$a^{2} - b^{2} = a^{2} - a b + a b - b^{2} = a (a - b) + b (a - b) = (a - b) (a + b)$
Hence, $a^{2} - b^{2}$ is equal to $(a - b) (a + b)$ .