Simplify (h-k)^2-k^2

${(h - k)}^{2} - k^{2}$

Simplify each term.

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Rewrite ${(h - k)}^{2}$ as $(h - k) (h - k)$ .

$(h - k) (h - k) - k^{2}$

Expand $(h - k) (h - k)$ using the FOIL Method.

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Apply the distributive property.

$h (h - k) - k (h - k) - k^{2}$

Apply the distributive property.

$h \cdot h + h (- k) - k (h - k) - k^{2}$

Apply the distributive property.

$h \cdot h + h (- k) - k h - k (- k) - k^{2}$

Simplify and combine like terms.

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Simplify each term.

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Multiply $h$ by $h$ .

$h^{2} + h (- k) - k h - k (- k) - k^{2}$

Rewrite using the commutative property of multiplication.

$h^{2} - h k - k h - k (- k) - k^{2}$

Multiply $k$ by $k$ .

$h^{2} - h k - k h - 1 \cdot - 1 k^{2} - k^{2}$

Multiply $- 1$ by $- 1$ .

$h^{2} - h k - k h + 1 k^{2} - k^{2}$

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

$h^{2} - h k - k h + k^{2} - k^{2}$

Subtract $k h$ from $- h k$ .

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Move $k$ .

$h^{2} - h k - 1 h k + k^{2} - k^{2}$

Subtract $h k$ from $- h k$ .

$h^{2} - 2 h k + k^{2} - k^{2}$

Combine the opposite terms in $h^{2} - 2 h k + k^{2} - k^{2}$ .

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Subtract $k^{2}$ from $k^{2}$ .

$h^{2} - 2 h k + 0$

Add $h^{2} - 2 h k$ and $0$ .

$h^{2} - 2 h k$

Simplify (h-k)^2-k^2

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