Hank’s teacher asked him to verify that the product (y−3)(y2+3y+9) is a difference of cubes. He used the distributive property to multiply the binomial times the trinomial. Before simplifying, his product was a polynomial of the form y3+3y2+ay−3y2−ay−27. What is the value of a in the polynomial? 3 9 18 27

Step-by-step explanation:

A., Is the correct answer. I just took it.

A is the coefficient

a = 9

Step-by-step explanation:

In the product (y−3)(y2+3y+9), we can get the first degree term of y in two ways,

y*(9), or -3*(3y)value in parentheses are from the second factor

therefore a = 9

As we can see in his simplification there are 2 pairs of terms that negate each other because of oposite sign which will leave us with y^3 - 27 which is indeed difference of cubes.

we can notice that first he multiplied y from binomial with each term in trinomial. third multiplication is y*9 which means that a = 9

Answer is 9

a = 9

Step-by-step explanation:

Let's work on the product to answer the question:

[tex](y-3)\,(y^2+3y+9)= y^3+3y^2+9y-3y^2-9y-27[/tex]

therefore the value of the requested "a" is 9

Assuming that the given polynomials are (y - 3) and (y^2 + 3y + 9), then the multiplication would yield the follow values below simplifying:

y^3 + 3y^2 + 9y - 3y^2 - 9y - 27

As compared to what is being solved from above, the value of "a" is 9.

a = 9

Step-by-step explanation:

expand (y - 3)(y² + 3y + 9)

= y³ + 3y² + 9y - 3y² - 9y - 27

compare the coefficients of like terms with

y³ + 3y² + ay - 3y² - ay - 27

ay = 9y and - ay = - 9y ⇒ a = 9

C.

Step-by-step explanation:

edg.

The correct answer is 9