Basic Math Examples

$(m + 2 n^{2}) - 4 {(r + s)}^{2}$

Step 1

Rewrite ${(r + s)}^{2}$ as $(r + s) (r + s)$ .

$m + 2 n^{2} - 4 ((r + s) (r + s))$

Step 2

Expand $(r + s) (r + s)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$m + 2 n^{2} - 4 (r (r + s) + s (r + s))$

Step 2.2

Apply the distributive property.

$m + 2 n^{2} - 4 (r \cdot r + r s + s (r + s))$

Step 2.3

Apply the distributive property.

$m + 2 n^{2} - 4 (r \cdot r + r s + s r + s \cdot s)$

$m + 2 n^{2} - 4 (r \cdot r + r s + s r + s \cdot s)$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $r$ by $r$ .

$m + 2 n^{2} - 4 (r^{2} + r s + s r + s \cdot s)$

Step 3.1.2

Multiply $s$ by $s$ .

$m + 2 n^{2} - 4 (r^{2} + r s + s r + s^{2})$

$m + 2 n^{2} - 4 (r^{2} + r s + s r + s^{2})$

Step 3.2

Add $r s$ and $s r$ .

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Step 3.2.1

Reorder $s$ and $r$ .

$m + 2 n^{2} - 4 (r^{2} + r s + r s + s^{2})$

Step 3.2.2

Add $r s$ and $r s$ .

$m + 2 n^{2} - 4 (r^{2} + 2 r s + s^{2})$

$m + 2 n^{2} - 4 (r^{2} + 2 r s + s^{2})$

$m + 2 n^{2} - 4 (r^{2} + 2 r s + s^{2})$

Step 4

Apply the distributive property.

$m + 2 n^{2} - 4 r^{2} - 4 (2 r s) - 4 s^{2}$

Step 5

Multiply $2$ by $- 4$ .

$m + 2 n^{2} - 4 r^{2} - 8 (r s) - 4 s^{2}$

Step 6

Remove parentheses.

$m + 2 n^{2} - 4 r^{2} - 8 r s - 4 s^{2}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$