Question

7. Factorise:a4-1/b4​

Answer 1

SOLUTION

TO FACTORISE

$\displaystyle \sf{ {a}^{4} - \frac{1}{ {b}^{4} } }$

FORMULA TO BE IMPLEMENTED

We are aware of the formula that

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

EVALUATION

Here the given expression is

$\displaystyle \sf{ {a}^{4} - \frac{1}{ {b}^{4} } }$

We factorise it as below

$\displaystyle \sf{ = {( {a}^{2} )}^{2} - { \bigg( \frac{1}{ {b}^{2} } \bigg)}^{2} }$

$\displaystyle \sf{ = \bigg( {a}^{2} + \frac{1}{ {b}^{2} } \bigg)\bigg( {a}^{2} - \frac{1}{ {b}^{2} } \bigg)}$

$\displaystyle \sf{ = \bigg( {a}^{2} + \frac{1}{ {b}^{2} } \bigg)\bigg( a + \frac{1}{b} \bigg)\bigg( a - \frac{1}{b} \bigg)}$

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$1.$ Find the value of the expression a² – 2ab + b² for a = 1, b = 1

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2. to verify algebraic identity a2-b2=(a+b)(a-b)

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Answer 2

Step-by-step explanation:

SOLUTION

TO FACTORISE

$\displaystyle \sf{ {a}^{4} - \frac{1}{ {b}^{4} } }$

FORMULA TO BE IMPLEMENTED

We are aware of the formula that

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

EVALUATION

Here the given expression is

$\displaystyle \sf{ {a}^{4} - \frac{1}{ {b}^{4} } }$

We factorise it as below

$\displaystyle \sf{ = {( {a}^{2} )}^{2} - { \bigg( \frac{1}{ {b}^{2} } \bigg)}^{2} }$

$\displaystyle \sf{ = \bigg( {a}^{2} + \frac{1}{ {b}^{2} } \bigg)\bigg( {a}^{2} - \frac{1}{ {b}^{2} } \bigg)}$

$\displaystyle \sf{ = \bigg( {a}^{2} + \frac{1}{ {b}^{2} } \bigg)\bigg( a + \frac{1}{b} \bigg)\bigg( a - \frac{1}{b} \bigg)}$

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