Question

Find the coefficient of x^2 in the expansion of (2x-1)^7

Answer 1

(2x-1)^7
=(2x)^7+7(2x)^6(-1)+21(2x)^5(-1)^2+35(2x)^4(-1)^3+35(2x)^3(-1)^4+21(2x)(-1)^5+7(2x)(-1)^6+(-1)^7
=128x^7+7(64x^6)(-1)+21(32x^5)+35(16x^4)(-1)+35(8x^3)+21(4x^2)(-1)+14x-1
=128x^7-7(64x^6)+672x^5-35(16x^4)+280x^3-21(4x^2)+14x-1
=128x^7-448x^6+672x^5-560x^4+280x^3-84x^2+14x-1
The coefficient of x^2 is -84