Question

subtract the given polynomials using the vertical format.

1. $(5g^{2}+6g - 10)-(2g^{2}+2g + 9)$

rewrite subtraction as addition of the opposite, then add.
$+5g^{2} +6g -10$
$-(+2g^{2} +2g +9)$
$+5g^{2} +6g -10$
$-2g^{2} -2g -9$

Explanation:

Step1: Align like terms vertically

$$\begin{align*} &+5g^2 \quad +6g \quad -10 \\ &-2g^2 \quad -2g \quad -9 \\ \end{align*}$$

Step2: Add $g^2$ terms

$5g^2 - 2g^2 = 3g^2$

Step3: Add $g$ terms

$6g - 2g = 4g$

Step4: Add constant terms

$-10 - 9 = -19$

Step5: Combine all results

$3g^2 + 4g - 19$

Answer:

$3g^2 + 4g - 19$