Basic Math Examples

$(m - 8) (m + 8) (m^{2} - 64)$

Step 1

Expand $(m - 8) (m + 8)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$(m (m + 8) - 8 (m + 8)) (m^{2} - 64)$

Step 1.2

Apply the distributive property.

$(m \cdot m + m \cdot 8 - 8 (m + 8)) (m^{2} - 64)$

Step 1.3

Apply the distributive property.

$(m \cdot m + m \cdot 8 - 8 m - 8 \cdot 8) (m^{2} - 64)$

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in $m \cdot m + m \cdot 8 - 8 m - 8 \cdot 8$ .

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Step 2.1.1

Reorder the factors in the terms $m \cdot 8$ and $- 8 m$ .

$(m \cdot m + 8 m - 8 m - 8 \cdot 8) (m^{2} - 64)$

Step 2.1.2

Subtract $8 m$ from $8 m$ .

$(m \cdot m + 0 - 8 \cdot 8) (m^{2} - 64)$

Step 2.1.3

Add $m \cdot m$ and $0$ .

$(m \cdot m - 8 \cdot 8) (m^{2} - 64)$

Step 2.2

Simplify each term.

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Step 2.2.1

Multiply $m$ by $m$ .

$(m^{2} - 8 \cdot 8) (m^{2} - 64)$

Step 2.2.2

Multiply $- 8$ by $8$ .

$(m^{2} - 64) (m^{2} - 64)$

Step 3

Expand $(m^{2} - 64) (m^{2} - 64)$ using the FOIL Method.

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Step 3.1

Apply the distributive property.

$m^{2} (m^{2} - 64) - 64 (m^{2} - 64)$

Step 3.2

Apply the distributive property.

$m^{2} m^{2} + m^{2} \cdot - 64 - 64 (m^{2} - 64)$

Step 3.3

Apply the distributive property.

$m^{2} m^{2} + m^{2} \cdot - 64 - 64 m^{2} - 64 \cdot - 64$

Step 4

Simplify and combine like terms.

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Step 4.1

Simplify each term.

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Step 4.1.1

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

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Step 4.1.1.1

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

$m^{2 + 2} + m^{2} \cdot - 64 - 64 m^{2} - 64 \cdot - 64$

Step 4.1.1.2

Add $2$ and $2$ .

$m^{4} + m^{2} \cdot - 64 - 64 m^{2} - 64 \cdot - 64$

Step 4.1.2

Move $- 64$ to the left of $m^{2}$ .

$m^{4} - 64 \cdot m^{2} - 64 m^{2} - 64 \cdot - 64$

Step 4.1.3

Multiply $- 64$ by $- 64$ .

$m^{4} - 64 m^{2} - 64 m^{2} + 4096$

Step 4.2

Subtract $64 m^{2}$ from $- 64 m^{2}$ .

$m^{4} - 128 m^{2} + 4096$