Question

Select all the expressions that are equivalent to the polynomial below.

(4x+5)(-3x-1)

A (-16x2 + 10x - 3) + (4x2 - 29x - 2)
B 3(x - 5) - 2(6x2 + 9x + 5)
C 2(x - 1) - 3(4x2 + 7x + 1)
D (2x2 - 11x - 9) - (14x2 + 8x - 4)
E (-15x2 + 9x - 10) + (3x2 - 10x - 5)
F (4x2 - 13x - 7) - (16x2 + 9x - 5)

Answer 1

The answers are: D and C and A and E
because:


B 3(x - 5) - 2(6x2 + 9x + 5)=−12x^2−15x−25

F (4x2 - 13x - 7) - (16x2 + 9x - 5)=−12x2−22x−2

E (-15x2 + 9x - 10) + (3x2 - 10x - 5)=−12x^2−x−15

Answer 2

(A), (C) and (D)

Explanation:

The given expression is:

`(4x+5)(-3x-1)`

which can be simplified as:

=
`-12x^2-15x-4x-5`

=
`-12x^2-19x-5`

which is the required simplified expression.

(A) The expression is:

`(-16x^2+10x-3)+(4x^2-29x-2)`

=
`-16x^2+10x-3+4x^2-29x-2`

=
`-12x^2-19x-5`

which is equivalent to the given expression, thus this option is correct.

(B) The expression is:

`3(x-5)-2(6x^2+9x+5)`

=
`3x-15-12x^2-18x-10`

=
`-12x^2-15x-25`

which is not equivalent to the given expression, thus this option is incorrect.

(C) The expression is:

`2(x-1)-3(4x^2+7x+1)`

=
`2x-2-12x^2-21x-3`

=
`-12x^2-19x-5`

which is equivalent to the given expression, thus this option is correct.

(D) The expression is:

`(2x^2-11x-9)-(14x^2+8x-4)`

=
`2x^2-11x-9-14x^2-8x+4`

=
`-12x^2-19x-5`

which is equivalent to the given expression, thus this option is correct.

(E) The expression is:

`(-15x^2+9x-10)+(3x^2-10x-5)`

=
`-15x^2+9x-10+3x^2-10x-5`

=
`-12x^2-x-15`

which is not equivalent to the given expression, thus this option is incorrect

(F) The expression is:

`(4x^2-13x-7)-(16x^2+9x-5)`

=
`4x^2-13x-7-16x^2-9x+5`

=
`-12x^2-22x-2`

which is not equivalent to the given expression, thus this option is incorrect.