If a + b = 1, then a4 + b4 - a3 - b3 - 2a2b2 + ab is equal to - Zigya

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If a + b = 1, then a⁴ + b⁴ - a³ - b³ - 2a²b² + ab is equal to

1

2

4

4

D.

4

straight a to the power of 4 plus straight b to the power of 4 minus straight a cubed minus straight b cubed minus 2 straight a squared straight b squared plus ab

equals straight a to the power of 4 plus straight b to the power of 4 minus 2 straight a squared straight b squared minus straight a cubed minus straight b cubed plus ab equals space left parenthesis straight a squared minus straight b squared right parenthesis squared space minus space left parenthesis straight a cubed plus straight b cubed right parenthesis space plus space ab equals space left parenthesis straight a plus straight b right parenthesis squared space left parenthesis straight a minus straight b right parenthesis squared space minus space left parenthesis straight a plus straight b right parenthesis thin space left parenthesis straight a squared minus ab plus straight b squared right parenthesis plus ab

equals space left parenthesis straight a minus straight b right parenthesis squared minus straight a squared plus ab minus straight b squared plus ab space space space space left square bracket because space space straight a space plus space straight b space equals space 1 right square bracket equals space left parenthesis straight a minus straight b right parenthesis squared space minus space left parenthesis straight a minus straight b right parenthesis squared space equals space 0

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