Question

Which of the following expression is equivalent to 6x2−13x−28

I. 6x2+8x−21x−28
II. 2x(3x+4)+7x(3x−4)
III. 2x(3x+4)−7(3x+4)
IV. (3x+4)(2x−7)

IV only
IV only

I, III, and IV
I, III, and IV

I, II, and IV
I, II, and IV

I and IV only
I and IV only

Answer 1

I, III and IV

Explanation:

Required

Determine equivalent expressions to
`6x^2 - 13x - 28`

To do this, we simplify each of the given options.

`I.\ 6x2+8x-21x-28`

Simplify like terms

`6x2+8x-21x-28`

`= 6x2-13x-28`

This is equivalent to the given expression

`II.\ 2x(3x + 4) + 7x(3x - 4)`

Open Bracket

`2x(3x + 4) + 7x(3x - 4)`

`2x*3x + 2x*4 + 7x*3x - 7x*4`

`6x^2 + 8x - 21x^2 - 28x`

Collect Like Terms

`6x^2 - 21x^2 + 8x - 28x`

`-15x^2 - 20x`

This is not equivalent to the given expression

`III.\ 2x(3x+4)-7(3x+4)`

Open Bracket

`2x(3x+4)-7(3x+4)`

`2x*3x + 2x*4 - 7*3x - 7*4`

`6x^2 + 8x - 21x - 28`

Simplify Like Terms

`6x^2 -13x - 28`

This is equivalent to the given expression

`IV.\ (3x + 4)(2x-7)`

Open Brackets

`3x * 2x - 3x * 7 + 4*2x-4*7`

`6x^2 - 21x+ 8x-21`

Simplify like terms

`6x^2 -13x-21`

This is equivalent to the given expression

Hence: I, III and IV are equivalent to the given expression