Basic Math Examples

${(- 2 r^{2} + s^{2})}^{2}$

Step 1

Rewrite ${(- 2 r^{2} + s^{2})}^{2}$ as $(- 2 r^{2} + s^{2}) (- 2 r^{2} + s^{2})$ .

$(- 2 r^{2} + s^{2}) (- 2 r^{2} + s^{2})$

Step 2

Expand $(- 2 r^{2} + s^{2}) (- 2 r^{2} + s^{2})$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$- 2 r^{2} (- 2 r^{2} + s^{2}) + s^{2} (- 2 r^{2} + s^{2})$

Step 2.2

Apply the distributive property.

$- 2 r^{2} (- 2 r^{2}) - 2 r^{2} s^{2} + s^{2} (- 2 r^{2} + s^{2})$

Step 2.3

Apply the distributive property.

$- 2 r^{2} (- 2 r^{2}) - 2 r^{2} s^{2} + s^{2} (- 2 r^{2}) + s^{2} s^{2}$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Rewrite using the commutative property of multiplication.

$- 2 \cdot - 2 r^{2} r^{2} - 2 r^{2} s^{2} + s^{2} (- 2 r^{2}) + s^{2} s^{2}$

Step 3.1.2

Multiply $r^{2}$ by $r^{2}$ by adding the exponents.

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Step 3.1.2.1

Move $r^{2}$ .

$- 2 \cdot - 2 (r^{2} r^{2}) - 2 r^{2} s^{2} + s^{2} (- 2 r^{2}) + s^{2} s^{2}$

Step 3.1.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 2 \cdot - 2 r^{2 + 2} - 2 r^{2} s^{2} + s^{2} (- 2 r^{2}) + s^{2} s^{2}$

Step 3.1.2.3

Add $2$ and $2$ .

$- 2 \cdot - 2 r^{4} - 2 r^{2} s^{2} + s^{2} (- 2 r^{2}) + s^{2} s^{2}$

Step 3.1.3

Multiply $- 2$ by $- 2$ .

$4 r^{4} - 2 r^{2} s^{2} + s^{2} (- 2 r^{2}) + s^{2} s^{2}$

Step 3.1.4

Rewrite using the commutative property of multiplication.

$4 r^{4} - 2 r^{2} s^{2} - 2 s^{2} r^{2} + s^{2} s^{2}$

Step 3.1.5

Multiply $s^{2}$ by $s^{2}$ by adding the exponents.

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Step 3.1.5.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4 r^{4} - 2 r^{2} s^{2} - 2 s^{2} r^{2} + s^{2 + 2}$

Step 3.1.5.2

Add $2$ and $2$ .

$4 r^{4} - 2 r^{2} s^{2} - 2 s^{2} r^{2} + s^{4}$

Step 3.2

Subtract $2 s^{2} r^{2}$ from $- 2 r^{2} s^{2}$ .

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Step 3.2.1

Move $s^{2}$ .

$4 r^{4} - 2 r^{2} s^{2} - 2 r^{2} s^{2} + s^{4}$

Step 3.2.2

Subtract $2 r^{2} s^{2}$ from $- 2 r^{2} s^{2}$ .

$4 r^{4} - 4 r^{2} s^{2} + s^{4}$