Match each binomial expression with the set of coefficient of the term obtain by expanding the expression

I   ...  3

II ...  4

III  ...  2

IV ... 1

Step-by-step explanation:

Recall binomial theorem as

(x+y)^n = x^n+nCr x^(n-1)Y++y^n

Using the above we find that

(x+y)^4 = x^4+4x^3+6x^2+4x+1

Hence 4 matches with 1.

Next option 27,54,36,8

are from (3x+2y)^3 because

(3x+2y)^3 = 27x^3+8y^3+18xy(3x+2y)

Option 2 for question 3.

Next is (2x+y)^3 will have 4 terms with coefficients as

8, 12,6,1

So I question for option 4.

The last question 2 = (2x+3y)^4

= (2x)^4+4(2x)^3(3y) + 6(2x)^2(3y)^2+4(2x)(3y)^3+(3y)^4

Hence coefficients are 16,96, 216,216 and 81

I   ...  3

II ...  4

III  ...  2

IV ... 1

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500