Question

factoring 9x² - (x²- 4) ²​

Answer 1

$\huge{\underline{\underline{\red{♡Answer→}}}}$

$9 {x}^{2} - {( {x}^{2} - 4)}^{2} \\ = ( {3x)}^{2} - ( { {x}^{2} - 4) }^{2}$

Use the identity →

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

$= (3x + ( {x}^{2} + 4))(3x - ( {x}^{2} - 4)) \\ = (3x + {x}^{2} + 4)(3x - {x}^{2} + 4) \\ = ( {x}^{2} + 3x + 4)( - {x}^{2} + 3x + 4) \\ = ( {x}^{2} + 3x + 4)( - {x}^{2} + 4x - x + 4) \\ = ( {x}^{2} + 3x + 4)( - x(x - 4) - 1(x - 4)) \\ = ( {x}^{2} + 3x + 4)( - x - 1)(x - 4)$

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