Answer:
1 - 12x + 60x^2 - 160x^3 + 240x^4 - 192x^5 + 64x^6
Explanation:
So we need to know the 7th line of pascals triangle so let us write it out
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1 <----- This one
Now we know we will need coefficients of x from 0 to 6, let us call this i, and for each of these the coefficient is
(-2)^i * (1)^(6-i) * number in pascals triangle
Hence
i = 0, 1 * 1 * 1 = 1
i = 1, -2 * 1 * 6 = -12
i = 2, 4 * 1 * 15 = 60
i = 3, -8 * 1 * 20 = -160
i = 4, 16 * 1 * 15 = 240
i = 5, -32 * 1 * 6 = -192
i = 6, 64 * 1 * 1 = 64
Hence (1-2x)^6 = 1 - 12x + 60x^2 - 160x^3 + 240x^4 - 192x^5 + 64x^6