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

Answer:

I, III and IV

Step-by-step 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