Question

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

Answer 1

$(2x+y)^3$ = $8x^3+12x^2y+6xy^2+y^3$

The coefficients are  8 , 12, 6, 1

$(2x+3y)^4$= $16x^4+96x^3y+216x^2y^2+216xy^3+81y^4$

The coefficients are  16, 96, 216, 216, 81

$(3x+2y)^3$=$27x^3+54x^2y+36xy^2+8y^3$

The coefficients are  27, 54,36 , 8

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

The coefficients are 1, 4, 6, 4, 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.