Question

Use the chart to multiply the binomial by the trinomial.

What is the product?
A.y3 + 27
B.y3 – 27
C.y3 – 6y2 + 27
D.y3 + 6y2 + 27

Answer 1

(y + 3)(y^2 - 3y + 9) =
y(y^2 - 3y + 9) + 3(y^2 - 3y + 9) =
y^3 - 3y^2 + 9y + 3y^2 - 9y + 27 =
y^3 + 27 <==

Answer 2

option (1) is correct.

the product of the binomial by the trinomial is
`y^3+27`.

Explanation:

Binomial is the term having two different term and trinomial having three different terms.

Here, Binomial is
`y+3` and trinomial is
`y^2-3y+9`

We have find the product of the binomial by the trinomial.

`(y+3)(y^2-3y+9)`

Multiply each term of binomial with trinomial,

`\Rightarrow y(y^2-3y+9)+3(y^2-3y+9)`

`\Rightarrow y^3-3y^2+9y+3y^2-9y+27`

Combining like term, we get,

`\Rightarrow y^3+(3-3)y^2+(9-9)y+27`

`\Rightarrow y^3+27`

Thus, the product of the binomial by the trinomial is
`y^3+27`.

Hence, option (1) is correct.