Question

the value of(2+w)(2+w^2)(2-w^2)(2-w^4) is

Answer 1

Answer: w^{9} + 2 w^{8}- 6 w^{5}- 12 w^{4} + 8 w + 16

Step-by-step explanation:

((2+w)(2+w 2 ))(2−w2 )(2−w4 )

= (w3 +2w2 +2w+4)(2−w2 )(2−w4 )

= (−w5 −2w  +4w+8)(2−w4 )

= (−w5 −2w4 +4w+8)⋅2−(−w5 -2w4+4w+8)w4

= −2w5 −4w4 +8w+16+w9 +2w8 −4w5 −8w  4

= (−6)w  5 +(−12)w4 +8w+16+w9 +2w8

= w^{9} + 2 w^{8}- 6 w^{5}- 12 w^{4} + 8 w + 16

Answer 2

Step-by-step explanation:

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