Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

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

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Step 1.2.1

Apply the distributive property.

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

Step 1.2.2

Apply the distributive property.

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

Step 1.2.3

Apply the distributive property.

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

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply $h$ by $h$ .

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

Step 1.3.1.2

Rewrite using the commutative property of multiplication.

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

Step 1.3.1.3

Rewrite using the commutative property of multiplication.

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

Step 1.3.1.4

Multiply $k$ by $k$ by adding the exponents.

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Step 1.3.1.4.1

Move $k$ .

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

Step 1.3.1.4.2

Multiply $k$ by $k$ .

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

Step 1.3.1.5

Multiply $- 1$ by $- 1$ .

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

Step 1.3.1.6

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

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

Step 1.3.2

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

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Step 1.3.2.1

Move $k$ .

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

Step 1.3.2.2

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

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

$h^{2} - 2 h k$