State whether the statement is True or False-Expand- a-1a3 is a3-3a-3a-1a3-

The correct option is A True (a+b) ^ 3 = a ^ 3 +b^ 3 +3a^ 2 b+3ab^ 2 (a+ 1 / a )^ 3 = a^ 3 + 1 / a^ 3 + 3 / a +3a ...

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Simplification of an Expression

State whether...

Question

State whether the statement is True or False.
Expand: $(a + \frac{1}{a})^{3}$ is $a^{3} + 3 a + \frac{3}{a} + \frac{1}{a^{3}}$ .

True

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False

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Solution

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(a - 2 b)^{3}

a^{3} - 6 a^{2} b + 12 a b^{2} - 8 b^{3}

{(a + b + c)}^{3} - a^{3} - b^{3} - c^{3} = 3 (a + b) (b + c) (c + a)

{(a + \frac{1}{a})}^{2} = 3

a \neq 0

a^{3} + \frac{1}{a^{3}} = 0

a + \frac{1}{a} = p

a \neq 0

a^{3} + \frac{1}{a^{3}} = p (p^{2} - 3)

\frac{a}{b} + \frac{b}{a} = - 1

a^{3} - b^{3} = 0

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