Question

Use Pascal’s Triangle to expand the binomial.
( d – 4)^6
Also show your steps.

Answer 1

do you know pascals triangle?

Answer 2

I know them alittle

Answer 3

i wont write it all out but first 4 lines are

1
1 1
1 2 1
1 3 3 1

notice how its formed by adding the 2 numbers eg 1 + 2 giving 3 on next line
the last line gives the coefficients of x in expansion of ( x + 1^)3

Answer 4

the 6th line for expansions of ( ax + a)^6 iS

1 6 15 20 15 6 1

Answer 5

* (x + a)^2

Answer 6

How do you expand it

Answer 7

ok
( d - 4)^6

= 1d^6*(-4)^0 + 6 d^5*(-4)^1 + 15 d^4*(-4)^2 + ..

do you see the pattern? - the numbers 1, 6 and 15 from Pascals Triangles and
the exponents of d starting at 6 and the going down by 1 to 5 and then to 4,
and those of (-4) starting at 0 then ascending to 1 then 2,
and the total of exponents always adding up to 6.

Answer 8

then simplify :
= d^6 - 24d^5 + 240d^4+...

Answer 9

Thanks, I really appreciate you help, that was the part i did not get.

Answer 10

ok welcome