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The terms that come from expansion through Pascal's Triangle are x^3+9x^2+27x+27. The third term in this sequence is 27x. This is your answer.

The third term of the expansion of [tex](x+3)^{3}[/tex] using Pascal's Triangle is 27x.

What is Pascal's Triangle?

The array of numbers is known as Pascal's triangle. It is developed by a French Mathematician Blaise Pascal.

How to determine third term of the expression?

He had given a binomial theorem according to which an expression can be opened through the following formula:

[tex](a+b)^{n} = nC0a^{n} +nC1a^{n-1} b+nC2a^{n-2}b^{2}+.......+nCnb^{n}[/tex]

So, to determine the third term of the expression we need to solve [tex]3C2x^{1}3^{2}[/tex]

we know that nCr =n!/r!(n-r)!

[tex]3C2x^{1}3^{2}[/tex] =3!/2!(9x)

            =3*2!/2!(9x)

            =27x

Hence the third term of the expression [tex](x+3)^{3}[/tex] is 27x.

Learn more about combinations on https://brainly.com/question/11732255

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