Question

subtract $5x^3 - 3x + 4$ from $7x^3 + 2x - 6$.
a. $12x^3 - x - 2$
b. $2x^3 - 5x + 10$
c. $2x^3 + 5x - 10$
d. $2x^3 - 5x - 10$

Explanation:

Step1: Write the subtraction expression

$$(7x^3 + 2x - 6) - (5x^3 - 3x + 4)$$

Step2: Distribute the negative sign

$$7x^3 + 2x - 6 - 5x^3 + 3x - 4$$

Step3: Combine like terms for $x^3$

$$(7x^3 - 5x^3) + 2x - 6 + 3x - 4 = 2x^3 + 2x - 6 + 3x - 4$$

Step4: Combine like terms for $x$

$$2x^3 + (2x + 3x) - 6 - 4 = 2x^3 + 5x - 6 - 4$$

Step5: Combine constant terms

$$2x^3 + 5x + (-6 - 4) = 2x^3 + 5x - 10$$

Answer:

c. $2x^3 + 5x - 10$