Basic Math Examples

$9 r^{2} s + 4 r s + 5 s^{2} - 9 r^{2} + 2 r^{2} s - 5 r s - s^{2} + 20 r^{2} + r s + 5 s^{2}$

Step 1

Add $9 r^{2} s$ and $2 r^{2} s$ .

$4 r s + 5 s^{2} - 9 r^{2} + 11 r^{2} s - 5 r s - s^{2} + 20 r^{2} + r s + 5 s^{2}$

Step 2

Subtract $5 r s$ from $4 r s$ .

$5 s^{2} - 9 r^{2} + 11 r^{2} s - r s - s^{2} + 20 r^{2} + r s + 5 s^{2}$

Step 3

Combine the opposite terms in $5 s^{2} - 9 r^{2} + 11 r^{2} s - r s - s^{2} + 20 r^{2} + r s + 5 s^{2}$ .

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Step 3.1

Add $- r s$ and $r s$ .

$5 s^{2} - 9 r^{2} + 11 r^{2} s - s^{2} + 20 r^{2} + 0 + 5 s^{2}$

Step 3.2

Add $5 s^{2} - 9 r^{2} + 11 r^{2} s - s^{2} + 20 r^{2}$ and $0$ .

$5 s^{2} - 9 r^{2} + 11 r^{2} s - s^{2} + 20 r^{2} + 5 s^{2}$

Step 4

Subtract $s^{2}$ from $5 s^{2}$ .

$4 s^{2} - 9 r^{2} + 11 r^{2} s + 20 r^{2} + 5 s^{2}$

Step 5

Add $4 s^{2}$ and $5 s^{2}$ .

$- 9 r^{2} + 11 r^{2} s + 20 r^{2} + 9 s^{2}$

Step 6

Add $- 9 r^{2}$ and $20 r^{2}$ .

$11 r^{2} + 11 r^{2} s + 9 s^{2}$

Step 7

Reorder $11 r^{2}$ and $11 r^{2} s$ .

$11 r^{2} s + 11 r^{2} + 9 s^{2}$