Expand the following using the binomial theorem and pascal’s triangle. (x + 2)6 (x − 4)4 (2x + 3)5 (2x − 3y)4 in the expansion of (3a + 4b)8, which of the following are possible variable terms? explain your reasoning. a2b3; a5b3; ab8; b8; a4b4; a8; ab7; a6b5

The possible terms are .

Step-by-step explanation:

Binomial Theorem:

Using Binomial Theorem, we get

Similarly,

The Pascal’s triangle is given below. In Pascal’s triangle nth row represents the coefficients of the expression of .

In the expression , a=x, b=2 and n=6. Using 7th row of Pascal’s triangle we get

Similarly,

In a=x, b=-4 and n=4. Using 5th row of Pascal’s triangle we get

In a=2x, b=3 and n=5. Using 6th row of Pascal’s triangle we get

In a=2x, b=-3y and n=4. Using 5th row of Pascal’s triangle we get

In binomial expansion of the degree of each term must be 8. It means the sum of powers of a and b is equal to 8.

For the dgree of term is 2+3=5. So, it is not possible variable term.

Therefore the possible terms are .

(1,4) is on graph of f(x)

f(1) = 4

so 1/4 f(x)

1/4 f(1)

1/4. ×4

1

so point for function 1/4. f(x) is (1,1)