where C(n,r) is the binomial coefficient "n choose r".
To find the coefficient of the last term in this expansion, we need to look at the term that contains the variable x⁷, which is the last term in the expansion. This term is:
1*C(7,7)*2⁰*(-x)⁷ = -x⁷
Therefore, the coefficient of the last term in the expansion of (2-x)⁷ is -1.
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Verified answer
The expansion of the binomial (2-x)⁷ can be found using the binomial theorem, which states that:
(2-x)⁷ = 1*C(7,0)*2⁷*(-x)⁰ + 7*C(7,1)*2⁶*(-x)¹ + 21*C(7,2)*2⁵*(-x)² + 35*C(7,3)*2⁴*(-x)³ + 35*C(7,4)*2³*(-x)⁴ + 21*C(7,5)*2²*(-x)⁵ + 7*C(7,6)*2¹*(-x)⁶ + 1*C(7,7)*2⁰*(-x)⁷
where C(n,r) is the binomial coefficient "n choose r".
To find the coefficient of the last term in this expansion, we need to look at the term that contains the variable x⁷, which is the last term in the expansion. This term is:
1*C(7,7)*2⁰*(-x)⁷ = -x⁷
Therefore, the coefficient of the last term in the expansion of (2-x)⁷ is -1.