Expand the binomial (1 - 2x)^6 use pascal’s triangle

1 - 12x + 60x^2 - 160x^3 + 240x^4 - 192x^5 + 64x^6

Step-by-step 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

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3

4

step-by-step explanation:

6 (donuts) divided by 3 is 2.

so 2/3 means 2 times 2, which is 4/6.

you get two and your friend gets four.