Question

what is the simplified form of (2x^2 4x - 3) (3x 1)? a) 6x^3 10x^2 - 5x 3 b) 6x^3 14x 5x - 3 c) 6x^3 14x^2 - 5x - 3 d) 6x^3 - 10x^2 - 5x - 3

Answer 1

6x^3 + 14x^2 - 5x - 3
Do you know of the FOIL method?

Answer 2

Option (c) is correct.

The simplified form of
`(2x^2+4x-3)(3x+1)` is
`6x^3+14x^2-5x-3`

Explanation:

Given :
`(2x^2+4x-3)(3x+1)`

We have to write the given product in simplified form and choose correct option from the given options.

Consider
`\left(2x^2+4x-3\right)\left(3x\:+1\right)`

Multiply each term of first bracket with each term of second bracket, we get,

`=2x^2\cdot \:3x+2x^2\cdot \:1+4x\cdot \:3x+4x\cdot \:1+\left(-3\right)\cdot \:3x+\left(-3\right)\cdot \:1`

Apply minus plus rule
`+\left(-a\right)=-a` , we get,

`=2\cdot \:3x^2x+2\cdot \:1\cdot \:x^2+4\cdot \:3xx+4\cdot \:1\cdot \:x-3\cdot \:3x-3\cdot \:1`

On simplifying, we get,

Adding similar terms,

`4x-9x=-5x\\\\\\ and\ 2x^2+12x^2=14x^2`

`=6x^3+14x^2-5x-3`

Thus, option (c) is correct.

The simplified form of
`(2x^2+4x-3)(3x+1)` is
`6x^3+14x^2-5x-3`