Basic Math Examples

$9 a^{2} - a y + y^{2} + (- a^{2} - 3 a y + 4 y^{2})$

Step 1

Remove parentheses.

$9 a^{2} - a y + y^{2} - a^{2} - 3 a y + 4 y^{2}$

Step 2

Regroup terms.

$- a y - 3 a y + 9 a^{2} + y^{2} - a^{2} + 4 y^{2}$

Step 3

Subtract $3 a y$ from $- a y$ .

$- 4 a y + 9 a^{2} + y^{2} - a^{2} + 4 y^{2}$

Step 4

Subtract $a^{2}$ from $9 a^{2}$ .

$- 4 a y + 8 a^{2} + y^{2} + 4 y^{2}$

Step 5

Add $y^{2}$ and $4 y^{2}$ .

$- 4 a y + 8 a^{2} + 5 y^{2}$

Step 6

Factor $- 1$ out of $- 4 a y + 8 a^{2} + 5 y^{2}$ .

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Step 6.1

Reorder $- 4 a y$ and $8 a^{2}$ .

$8 a^{2} - 4 a y + 5 y^{2}$

Step 6.2

Factor $- 1$ out of $8 a^{2}$ .

$- (- 8 a^{2}) - 4 a y + 5 y^{2}$

Step 6.3

Factor $- 1$ out of $- 4 a y$ .

$- (- 8 a^{2}) - (4 a y) + 5 y^{2}$

Step 6.4

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

$- (- 8 a^{2}) - (4 a y) - (- 5 y^{2})$

Step 6.5

Factor $- 1$ out of $- (- 8 a^{2}) - (4 a y)$ .

$- (- 8 a^{2} + 4 a y) - (- 5 y^{2})$

Step 6.6

Factor $- 1$ out of $- (- 8 a^{2} + 4 a y) - (- 5 y^{2})$ .

$- (- 8 a^{2} + 4 a y - 5 y^{2})$

Step 7

Factor.

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Step 7.1

Factor $- 1$ out of $- 8 a^{2} + 4 a y - 5 y^{2}$ .

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Step 7.1.1

Factor $- 1$ out of $- 8 a^{2}$ .

$- (- (8 a^{2}) + 4 a y - 5 y^{2})$

Step 7.1.2

Factor $- 1$ out of $4 a y$ .

$- (- (8 a^{2}) - (- 4 a y) - 5 y^{2})$

Step 7.1.3

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

$- (- (8 a^{2}) - (- 4 a y) - (5 y^{2}))$

Step 7.1.4

Factor $- 1$ out of $- (8 a^{2}) - (- 4 a y)$ .

$- (- (8 a^{2} - 4 a y) - (5 y^{2}))$

Step 7.1.5

Factor $- 1$ out of $- (8 a^{2} - 4 a y) - (5 y^{2})$ .

$- - (8 a^{2} - 4 a y + 5 y^{2})$

Step 7.2

Remove unnecessary parentheses.

$- - 1 (8 a^{2} - 4 a y + 5 y^{2})$

Step 8

Combine exponents.

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Step 8.1

Factor out negative.

$- - (8 a^{2} - 4 a y + 5 y^{2})$

Step 8.2

Multiply $- 1$ by $- 1$ .

$1 (8 a^{2} - 4 a y + 5 y^{2})$

Step 8.3

Multiply $8 a^{2} - 4 a y + 5 y^{2}$ by $1$ .

$8 a^{2} - 4 a y + 5 y^{2}$