Finite Math Examples

$(3 x^{2} + 6 x y + 3 y^{2}) - (8 x^{2} - 6 x y - y^{2})$

Step 1

Apply the distributive property.

$3 x^{2} + 6 x y + 3 y^{2} - (8 x^{2}) - (- 6 x y) - - y^{2}$

Step 2

Simplify.

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Step 2.1

Multiply $8$ by $- 1$ .

$3 x^{2} + 6 x y + 3 y^{2} - 8 x^{2} - (- 6 x y) - - y^{2}$

Step 2.2

Multiply $- 6$ by $- 1$ .

$3 x^{2} + 6 x y + 3 y^{2} - 8 x^{2} + 6 (x y) - - y^{2}$

Step 2.3

Multiply $- - y^{2}$ .

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Step 2.3.1

Multiply $- 1$ by $- 1$ .

$3 x^{2} + 6 x y + 3 y^{2} - 8 x^{2} + 6 (x y) + 1 y^{2}$

Step 2.3.2

Multiply $y^{2}$ by $1$ .

$3 x^{2} + 6 x y + 3 y^{2} - 8 x^{2} + 6 (x y) + y^{2}$

Step 3

Remove parentheses.

$3 x^{2} + 6 x y + 3 y^{2} - 8 x^{2} + 6 x y + y^{2}$

Step 4

Subtract $8 x^{2}$ from $3 x^{2}$ .

$- 5 x^{2} + 6 x y + 3 y^{2} + 6 x y + y^{2}$

Step 5

Add $6 x y$ and $6 x y$ .

$- 5 x^{2} + 3 y^{2} + 12 x y + y^{2}$

Step 6

Add $3 y^{2}$ and $y^{2}$ .

$- 5 x^{2} + 4 y^{2} + 12 x y$

Step 7

Factor $- 1$ out of $- 5 x^{2} + 4 y^{2} + 12 x y$ .

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Step 7.1

Move $4 y^{2}$ .

$- 5 x^{2} + 12 x y + 4 y^{2}$

Step 7.2

Factor $- 1$ out of $- 5 x^{2}$ .

$- (5 x^{2}) + 12 x y + 4 y^{2}$

Step 7.3

Factor $- 1$ out of $12 x y$ .

$- (5 x^{2}) - (- 12 x y) + 4 y^{2}$

Step 7.4

Factor $- 1$ out of $4 y^{2}$ .

$- (5 x^{2}) - (- 12 x y) - (- 4 y^{2})$

Step 7.5

Factor $- 1$ out of $- (5 x^{2}) - (- 12 x y)$ .

$- (5 x^{2} - 12 x y) - (- 4 y^{2})$

Step 7.6

Factor $- 1$ out of $- (5 x^{2} - 12 x y) - (- 4 y^{2})$ .

$- (5 x^{2} - 12 x y - 4 y^{2})$