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Factorisation

Short Answer Type

61.
Factorise:

$space space straight a to the power of 4 space minus space straight b to the power of 4$

Using              a² - b² = (a - b) (a + b), we have

                     a⁴ - b⁴= (a²)² - (b²)²                               = $left parenthesis straight a squared space plus space straight b squared right parenthesis left parenthesis straight a squared space minus space straight b squared right parenthesis$

                            $equals left parenthesis straight a squared space plus space straight b squared right parenthesis left square bracket left parenthesis straight a space plus space straight b right parenthesis space left parenthesis straight a space minus space straight b right parenthesis right square bracket$

                              = $left parenthesis straight a squared space plus space straight b squared right parenthesis$ (a + b)(a - b)