Use pascal’s triangle to determine the second term of the expansion of (x + 2)^4.

Pascal triangle contains values as ; n being row number, and r is index in row, both 0 indexing. The second term in expansion of is

Pascal triangles contains coefficient of 's expanded form's terms.

For first row, we have:

Thus, 1 is the value in the first row of Pascal triangle.

Thus, for second row, we have:

The variable x has coefficient 1, and that 1 itself, so second row of Pascal triangle has 1 , 1 as values.

For third row, we have:

Thus, 1, 2, 1 as values in third row. And so on.

For nth row, and its rth term(all counted from 0-indexing(that means, counting of index starts from 0), then that term in Pascal triangle is

                  1

              1     1

            1     2     1

        1      3     3      1

  1        4      6     4       1

1        5      10    10     5       1

.........

The rth indexed term with nth row is termed as for expansion of

For the given condition, we've got  

We have n = 4, and r = 2 - 1 = 1(as second term needed, and second term is 1 indexed in 0 indexing).

Since y = 2, thus, the second term of  is

Thus,

The second term in expansion of is

Learn more about Pascal triangle here:

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10x³

Step-by-step explanation:

n=0                                  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

The second term of the expansion is: 5(a)³(b)

= 5(x)³(2)

= 10x³