Algebra Examples

$- 4 m^{2} (n^{2} - m^{2}) + 3 n^{2} (m^{2} - n^{2})$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$- 4 m^{2} n^{2} - 4 m^{2} (- m^{2}) + 3 n^{2} (m^{2} - n^{2})$

Step 1.2

Rewrite using the commutative property of multiplication.

$- 4 m^{2} n^{2} - 4 \cdot - 1 m^{2} m^{2} + 3 n^{2} (m^{2} - n^{2})$

Step 1.3

Simplify each term.

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Step 1.3.1

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

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Step 1.3.1.1

Move $m^{2}$ .

$- 4 m^{2} n^{2} - 4 \cdot - 1 (m^{2} m^{2}) + 3 n^{2} (m^{2} - n^{2})$

Step 1.3.1.2

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

$- 4 m^{2} n^{2} - 4 \cdot - 1 m^{2 + 2} + 3 n^{2} (m^{2} - n^{2})$

Step 1.3.1.3

Add $2$ and $2$ .

$- 4 m^{2} n^{2} - 4 \cdot - 1 m^{4} + 3 n^{2} (m^{2} - n^{2})$

Step 1.3.2

Multiply $- 4$ by $- 1$ .

$- 4 m^{2} n^{2} + 4 m^{4} + 3 n^{2} (m^{2} - n^{2})$

Step 1.4

Apply the distributive property.

$- 4 m^{2} n^{2} + 4 m^{4} + 3 n^{2} m^{2} + 3 n^{2} (- n^{2})$

Step 1.5

Rewrite using the commutative property of multiplication.

$- 4 m^{2} n^{2} + 4 m^{4} + 3 n^{2} m^{2} + 3 \cdot - 1 n^{2} n^{2}$

Step 1.6

Simplify each term.

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Step 1.6.1

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

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Step 1.6.1.1

Move $n^{2}$ .

$- 4 m^{2} n^{2} + 4 m^{4} + 3 n^{2} m^{2} + 3 \cdot - 1 (n^{2} n^{2})$

Step 1.6.1.2

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

$- 4 m^{2} n^{2} + 4 m^{4} + 3 n^{2} m^{2} + 3 \cdot - 1 n^{2 + 2}$

Step 1.6.1.3

Add $2$ and $2$ .

$- 4 m^{2} n^{2} + 4 m^{4} + 3 n^{2} m^{2} + 3 \cdot - 1 n^{4}$

Step 1.6.2

Multiply $3$ by $- 1$ .

$- 4 m^{2} n^{2} + 4 m^{4} + 3 n^{2} m^{2} - 3 n^{4}$

Step 2

Add $- 4 m^{2} n^{2}$ and $3 n^{2} m^{2}$ .

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Step 2.1

Move $n^{2}$ .

$4 m^{4} - 4 m^{2} n^{2} + 3 m^{2} n^{2} - 3 n^{4}$

Step 2.2

Add $- 4 m^{2} n^{2}$ and $3 m^{2} n^{2}$ .

$4 m^{4} - m^{2} n^{2} - 3 n^{4}$