Question

Select the correct product. ( x2 + 6 x + 9)(3 x - 1) 3 x3 + 17 x2 + 21 x - 9 3 x3 - 17 x2 - 21 x - 9 3 x3 + 19 x2 + 27 x + 9 3 x3 + 19 x2 + 9 x - 9

Answer 1

3x^3 + 17x^2 + 21x - 9

Explanation:

Use distributive property.

First distribute the 3x

3x times x^2 + 6x + 9. Distribute = 3x^3 + 18x^ 2 + 27x

Now we distribute the -1

-1 times x^2 + 6x + 9. Distribute = -x^2 -6x - 9

We Add both answers-

3x^3 + 18x^2 + 27x

+ -x^2 -6x - 9

__________________

3x^3 + 17x^2 + 21x - 9

Answer 2

`\boxed{ \bold{{ \boxed{ \sf{3 {x}^(3) + 17 {x}^(2) + 21x - 9}}}}}`

Option A is the correct option.

Explanation:

`\sf{( {x}^(2) + 6x + 9)(3x - 1)}`

Use distributive property

⇒
`{ \sf{ {x}^(2) (3x - 1) + 6x(3x - 1) + 9(3x - 1)}}`

⇒
`\sf{3 {x}^(3) - {x}^(2) + 18 {x}^(2) - 6x + 27x - 9}`

Collect like terms

⇒
`\sf{3 {x}^(3) + 17 {x}^(2) + 21x - 9}`

Hope I helped!

Best regards! :D