Question

select the correct answer.
find the difference.

$(3 - 13x - 7x^2) - (5x^2 + 12x - 10)$

a. $3x^2 - 25x - 2$
b. $-12x^2 - 25x + 13$
c. $-12x^2 - x - 7$
d. $-12x^2 - 25x - 7$

Explanation:

Step1: Distribute the negative sign

To subtract the second polynomial from the first, we distribute the negative sign to each term in the second polynomial:
$$(3 - 13x - 7x^2) - (5x^2 + 12x - 10) = 3 - 13x - 7x^2 - 5x^2 - 12x + 10$$

Step2: Combine like terms for \(x^2\) terms

Combine the \(x^2\) terms: \(-7x^2 - 5x^2 = -12x^2\)

Step3: Combine like terms for \(x\) terms

Combine the \(x\) terms: \(-13x - 12x = -25x\)

Step4: Combine like terms for constant terms

Combine the constant terms: \(3 + 10 = 13\)

Step5: Write the combined polynomial

Putting it all together, we get: \(-12x^2 - 25x + 13\)

Answer:

B. \(-12x^2 - 25x + 13\)