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Use Pascal's Triangle to expand the binomial. (d-3)^6

Sagot :

Using pascal triangle

(d-3)^6

Expoenent 6 has a coeffient of;

1 6 15 20 15 6 1

Hence;

[tex]d^6-6(d)^5(3)+15(d)^4(3)^2-20(d)^3(3)^3+15(d)^2(3)^4-6(d)(3)^5+3^6[/tex]

Two things to note here is that;

-There is a minus sign in-between the numbers in the bracket, hence we alternate the sign starting with positive

-secondly as the power of the first variable decreases the power of the second digit increases

We can further simplify;

[tex]d^{6\text{ }}-6d^5(3)+15(d)^4(9)^{}-20d^3(27)+15d^2(81)-6d(243)+729[/tex]

We will still simplify to give:

[tex]d^6-18d^5+135d^4-540d^3+1215d^2-1458d\text{ + 729}[/tex]

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