Algebra Examples

$(- 4 m^{2} + 5 m w - 12 w^{2})$ from $(- 10 m^{2} - 11 m w - 7 w^{2})$

Step 1

Write the problem as a mathematical expression.

$(- 10 m^{2} - 11 m w - 7 w^{2}) - (- 4 m^{2} + 5 m w - 12 w^{2})$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$- 10 m^{2} - 11 m w - 7 w^{2} - (- 4 m^{2}) - (5 m w) - (- 12 w^{2})$

Step 2.2

Simplify.

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Step 2.2.1

Multiply $- 4$ by $- 1$ .

$- 10 m^{2} - 11 m w - 7 w^{2} + 4 m^{2} - (5 m w) - (- 12 w^{2})$

Step 2.2.2

Multiply $5$ by $- 1$ .

$- 10 m^{2} - 11 m w - 7 w^{2} + 4 m^{2} - 5 (m w) - (- 12 w^{2})$

Step 2.2.3

Multiply $- 12$ by $- 1$ .

$- 10 m^{2} - 11 m w - 7 w^{2} + 4 m^{2} - 5 (m w) + 12 w^{2}$

$- 10 m^{2} - 11 m w - 7 w^{2} + 4 m^{2} - 5 m w + 12 w^{2}$

Step 3

Simplify by adding terms.

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Step 3.1

Add $- 10 m^{2}$ and $4 m^{2}$ .

$- 6 m^{2} - 11 m w - 7 w^{2} - 5 m w + 12 w^{2}$

Step 3.2

Subtract $5 m w$ from $- 11 m w$ .

$- 6 m^{2} - 7 w^{2} - 16 m w + 12 w^{2}$

Step 3.3

Add $- 7 w^{2}$ and $12 w^{2}$ .

$- 6 m^{2} + 5 w^{2} - 16 m w$