Algebra Examples

$(8 h^{2} - 5 h k + 6 k^{2}) - (- h^{2} + 7 h k - 2 k^{2})$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$8 h^{2} - 5 h k + 6 k^{2} - - h^{2} - (7 h k) - (- 2 k^{2})$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $- - h^{2}$ .

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Step 1.2.1.1

Multiply $- 1$ by $- 1$ .

$8 h^{2} - 5 h k + 6 k^{2} + 1 h^{2} - (7 h k) - (- 2 k^{2})$

Step 1.2.1.2

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

$8 h^{2} - 5 h k + 6 k^{2} + h^{2} - (7 h k) - (- 2 k^{2})$

Step 1.2.2

Multiply $7$ by $- 1$ .

$8 h^{2} - 5 h k + 6 k^{2} + h^{2} - 7 (h k) - (- 2 k^{2})$

Step 1.2.3

Multiply $- 2$ by $- 1$ .

$8 h^{2} - 5 h k + 6 k^{2} + h^{2} - 7 (h k) + 2 k^{2}$

$8 h^{2} - 5 h k + 6 k^{2} + h^{2} - 7 h k + 2 k^{2}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $8 h^{2}$ and $h^{2}$ .

$9 h^{2} - 5 h k + 6 k^{2} - 7 h k + 2 k^{2}$

Step 2.2

Subtract $7 h k$ from $- 5 h k$ .

$9 h^{2} + 6 k^{2} - 12 h k + 2 k^{2}$

Step 2.3

Add $6 k^{2}$ and $2 k^{2}$ .

$9 h^{2} + 8 k^{2} - 12 h k$