Question

What is the simplified form of the expression (3 - 13x - 7x²) - (5x² + 12x - 10)?

1) -12x² - 25x + 13
2) -12x² - 25x - 7
3) -12x² - x - 7
4) 3x² - 25x - 10

Answer 1

1) -12x² - 25x + 13

Step-by-step explanation:

(3 - 13x - 7x²) - (5x² + 12x - 10)

3 - 13x - 7x² - 5x² - 12x + 10 [Remove parentheses. Note the second set of numbers have reversed their signs since they were all multiplied by -1]

3 + 10 - 13x -12x - 7x² - 5x² [Group like terms]

13 - 25x - 12x² [Simplify]

Rearrange to match answer option 1)

-12x² - 25x + 13

1) -12x² - 25x + 13

Answer 2

To simplify the expression (3 - 13x - 7x²) - (5x² + 12x - 10), distribute the negative sign and combine like terms to get -12x² - 25x + 13.

Step-by-step explanation:

To simplify the expression (3 - 13x - 7x²) - (5x² + 12x - 10), we need to distribute the negative sign to each term inside the second parentheses. This gives us 3 - 13x - 7x² - 5x² - 12x + 10. Next, we can combine like terms by adding or subtracting the coefficients of the same degree variables. Combining the x² terms, we have -7x² - 5x² = -12x². Combining the x terms, we have -13x - 12x = -25x. And combining the constant terms, we have 3 + 10 = 13.

So the simplified form of the expression is -12x² - 25x + 13.