Question

Factorize: x⁴- y⁴ please solve this question its soo urgent ​

Answer 1

As we know that :

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

${x}^{4} - {y}^{4} = {( {x}^{2}) }^{2} - {( {y}^{2}) }^{2} \\ \\ = > ( {x}^{2} - {y}^{2} )( {x}^{2} + {y}^{2} ) \\ \\ = > (x - y)(x + y)( {x}^{2} + {y}^{2} )$

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I hope it will help you ☺

Fóllòw Më ❤

Answer 2

Question:

factorise x⁴ - y⁴

We know that:

$\sf\underbrace\red{ \: {a}^{2} - {b}^{2} = (a - b)(a + b)}$

So,

$\sf {x}^{4} - {y}^{4}$

=$\sf \: { ({x}^{2}) }^{2} - { ({y}^{2}) }^{2}$

Now using identity,we get:

$\sf { ({x}^{2}) }^{2} - { ({y}^{2} )}^{2}$

=$\sf \: ( {x}^{2} + {y}^{2})( {x}^{2} - {y}^{2} )$

again using the identity in (x² - y²),we get:

$\sf ({x}^{2} - {y}^{2} )$

=$\sf{(x - y)(x + y)}$

Thus,

$\sf{x}^{4} - {y}^{4}$

=$\sf{( {x}^{2} + {y}^{2} )(x - y)(x + y)}$

★ $\tt\underbrace{\overbrace\red{more\: algebraic\: identity}}$ ★

1) (a + b)² = a² + 2ab + b²

2) (a - b)² = a² - 2ab + b²

3) a² - b² = (a + b)(a - b)

4) (a + b)² = (a - b)² + 4ab

5) (a - b)² = (a + b)² - 4ab

6) (a + b)³ = a³ - 3ab(a - b) + b³

7) (a - b)³ = a³ + 3ab(a + b) + b³

8) a³ + b³ = (a + b)(a² - ab + b²)