Question

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

Answer 1

Answer:

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

Answer 2

By expanding the term $(2x+y)^3$, we get

$8x^3 + 12x^2y+6xy^2+y^3$.

Therefore, the coefficients for $(2x+y)^3$ are 8, 12, 6, 1.

By expanding the term $(2x+3y)^4$, we get

$16x^4+96x^3y+216x^2y^2+216xy^3+81y^4$.

Therefore, the coefficients for $(2x+3y)^4$ are 16, 96, 216, 216, 81.

By expanding the term $(3x+2y)^3$, we get

$27x^3+54x^2y+36xy^2+8y^3$.

Therefore, the coefficients for $(3x+2y)^3$ are 27, 54, 36, 8.

By expanding the term $(x+y)^4$, we get

$x^4+4x^3y+6x^2y^2+4xy^3+y^4$.

Therefore, the coefficients for $(x+y)^4$ are 1, 4, 6, 4, 1.