Question

Use pascal's triangle to expand the binomial (d-5y)^6 please show work

Answer 1

Pascals triangle to the 6th:
1                                     x^0
1 1                                  x^1
1 2 1                               x^2
1 3 3 1                           x^3
1 4 6 4 1                        x^4
1 5 10 10 5 1                x^5
1 6 15 20 15 6 1          x^6

the problem is to the 6th power so your going to use the 6th row of pascals triangle (don't count the first row). these numbers represent the coefficients of the variables

1(d-5y)^6 + 6(d-5y)^5 + 15(d-5y)^4 + 20(d-5y)^3 + 15(d-5y)^2 + 6(d-5y) + 1
then simplify

Answer 2

Answer:

$d^6 - 30 d^5 y + 375 d^4 y^2 - 2500 d^3 y^3 + 9375 d^2 y^4 - 18750 d y^5 + 15625 y^6$

Step-by-step explanation:

                    1                                 n=0

                 1    1                                n=1

            1      2     1                            n=2

         1      3     3       1                       n=3

      1    4      6      4        1                  n=4

   1   5    10     10        5     1                n=5

1    6     15     20     15     6      1          n=6

$(d-5y)^6$ we have exponent 6, so we use the numbers in pascals triangle where n=6

1    6     15     20     15     6      1  are the coefficients

$(a+b)^ 6 = 1a^6 + 6a^5b^1 + 15a^4b^2 +20a^3b^3 +15a^2b^4 +6a^1b^5 + 1b^6$

We have d in the place of 'a'  and -5y in the place of b

$(d-5y)^ 6 = 1d^6 + 6d^5(-5y)^1 + 15d^4(-5y)^2 +20d^3(-5y)^3 +15d^2(-5y)^4 +6d^1(-5y)^5 + 1(-5y)^6$

When we simplify the exponents it becomes

$d^6 - 30 d^5 y + 375 d^4 y^2 - 2500 d^3 y^3 + 9375 d^2 y^4 - 18750 d y^5 + 15625 y^6$