# How do you find the sum or difference of (8y-4y^2)+(3y-9y^2)?

Mar 3, 2017

$11 y - 13 {y}^{2}$

#### Explanation:

When adding or subtracting you can not mix 'types' (variables)

$\textcolor{b l u e}{\text{One method of several:}}$

$8 y - 4 {y}^{2}$
$\underline{3 y - 9 {y}^{2}} \leftarrow \text{ add}$
$11 y - 13 {y}^{2}$

$\textcolor{w h i t e}{}$

$\text{+++++++++++++++++++++++++++++++++++}$
$\text{+++++++++++++ "color(blue)("Additional teaching")" +++++++++}$
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$\textcolor{b r o w n}{\text{When multiplying numbers if the signs are the same the answer is}}$$\textcolor{b r o w n}{\text{positive. If the signs are different the answer is negative.}}$

$\left(8 y - 4 {y}^{2}\right) - \left(3 y - 9 {y}^{2}\right)$

Think of:
$\left(8 y - 4 {y}^{2}\right)$ as $+ 1 \left(8 y - 4 {y}^{2}\right)$

Multiply everything inside the bracket by +1 giving:

$8 y - 4 {y}^{2}$
..........................................................................

Think of:
$- \left(3 y - 9 {y}^{2}\right)$ as $- 1 \left(3 y - 9 {y}^{2}\right)$

Multiply everything inside $\left(3 y - 9 {y}^{2}\right)$ by -1 giving:

$- 3 y + 9 {y}^{2}$
.......................................................................
Sometimes it is helpful to think of add as 'put with' and subtract as 'remove from'

ul("Putting")" it all together ( put with "-> +") we have:"

$\textcolor{w h i t e}{. .} 8 y - 4 {y}^{2}$
$\underline{- 3 y + 9 {y}^{2}} \leftarrow \text{ add}$
$\textcolor{w h i t e}{. .} 5 y + 5 {y}^{2}$