JAMB - Mathematics (1981 - No. 36)
Multiply x2 + x + 1 by x2 - x + 1
x4 - x + x2
x4 - x2 + x2
x4 + x2 + 1
x4 + x2
Explanation
(x2 + x + 1)( x2 - x + 1)
= x2(x2 + x + 1) - x(x2 + x + 1) + (x3 + x + 1)
= x4 - x3 + x2 + x3 - x2 - x + 1
= x4 + x2 + 1
= x2(x2 + x + 1) - x(x2 + x + 1) + (x3 + x + 1)
= x4 - x3 + x2 + x3 - x2 - x + 1
= x4 + x2 + 1
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