Question

subtract the given polynomials using the vertical format.

1. $(7c^{3}-5c^{2}+2c)-(-3c^{3}+2c^{2}-2c)$

$\

$$\begin{matrix}+7c^{3}&-5c^{2}&+2c\\\\-(-3c^{3}&+2c^{2}&-2c)\\end{matrix}$$

$
rewrite subtraction as addition of the opposite, then add.

Explanation:

Step1: Rewrite subtraction as addition

Change signs of the second polynomial:
$$(7c^3 - 5c^2 + 2c) + (3c^3 - 2c^2 + 2c)$$

Step2: Align like terms vertically

$$\begin{align*} &+7c^3 -5c^2 +2c \\ +&+3c^3 -2c^2 +2c \\ \end{align*}$$

Step3: Add like terms (c³ terms)

$7c^3 + 3c^3 = 10c^3$

Step4: Add like terms (c² terms)

$-5c^2 + (-2c^2) = -7c^2$

Step5: Add like terms (c terms)

$2c + 2c = 4c$

Answer:

$10c^3 - 7c^2 + 4c$