Question

Find the difference. (3 - 13x - 7x2) - (5x2 12x - 10)

a. -12x2 - 25x - 7
b. -12x2 - 25x 13
c. -12x2 - x - 7
d. 3x2 - 25x - 2

Answer 1

Option (b) is correct.

The difference between two given polynomial is
`-12x^2-25x+13`

Explanation:

Given : Polynomial
`3 - 13x - 7x^2` and
`5x^2+ 12x - 10`

We have to find the difference between given two polynomial.

Consider Polynomial
`3 - 13x - 7x^2` and
`5x^2+ 12x - 10`

Difference is
`(3 - 13x - 7x^2)-(5x^2+ 12x - 10)`

Consider
`-\left(5x^2+12x-10\right)`

Distribute parentheses, we have,

`=-\left(5x^2\right)-\left(12x\right)-\left(-10\right)`

Apply plus- minus rule,

`-\left(-a\right)=a,\:\:\:-\left(a\right)=-a`

`=-5x^2-12x+10`

`=3-13x-7x^2-5x^2-12x+10`

Adding similar terms (terms having same variable with same power)

We have,

`=-12x^2-25x+13`

Thus, the difference between two given polynomial is
`-12x^2-25x+13`

Answer 2

To answer the question, distribute the negative sign and combine like terms.
3 - 13x - 7x² - 5x² - 12x + 10
(-7x² - 5x²) + (-13x - 12x) + (3 + 10)
Thus, the answer is letter B. -12x² - 25x + 13.