Basic Math Examples

$(3 n^{2} + 1) + {(8 n^{2} - 8)}^{2}$

Step 1

Simplify each term.

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Step 1.1

Rewrite ${(8 n^{2} - 8)}^{2}$ as $(8 n^{2} - 8) (8 n^{2} - 8)$ .

$3 n^{2} + 1 + (8 n^{2} - 8) (8 n^{2} - 8)$

Step 1.2

Expand $(8 n^{2} - 8) (8 n^{2} - 8)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$3 n^{2} + 1 + 8 n^{2} (8 n^{2} - 8) - 8 (8 n^{2} - 8)$

Step 1.2.2

Apply the distributive property.

$3 n^{2} + 1 + 8 n^{2} (8 n^{2}) + 8 n^{2} \cdot - 8 - 8 (8 n^{2} - 8)$

Step 1.2.3

Apply the distributive property.

$3 n^{2} + 1 + 8 n^{2} (8 n^{2}) + 8 n^{2} \cdot - 8 - 8 (8 n^{2}) - 8 \cdot - 8$

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

Rewrite using the commutative property of multiplication.

$3 n^{2} + 1 + 8 \cdot 8 n^{2} n^{2} + 8 n^{2} \cdot - 8 - 8 (8 n^{2}) - 8 \cdot - 8$

Step 1.3.1.2

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

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Step 1.3.1.2.1

Move $n^{2}$ .

$3 n^{2} + 1 + 8 \cdot 8 (n^{2} n^{2}) + 8 n^{2} \cdot - 8 - 8 (8 n^{2}) - 8 \cdot - 8$

Step 1.3.1.2.2

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

$3 n^{2} + 1 + 8 \cdot 8 n^{2 + 2} + 8 n^{2} \cdot - 8 - 8 (8 n^{2}) - 8 \cdot - 8$

Step 1.3.1.2.3

Add $2$ and $2$ .

$3 n^{2} + 1 + 8 \cdot 8 n^{4} + 8 n^{2} \cdot - 8 - 8 (8 n^{2}) - 8 \cdot - 8$

Step 1.3.1.3

Multiply $8$ by $8$ .

$3 n^{2} + 1 + 64 n^{4} + 8 n^{2} \cdot - 8 - 8 (8 n^{2}) - 8 \cdot - 8$

Step 1.3.1.4

Multiply $- 8$ by $8$ .

$3 n^{2} + 1 + 64 n^{4} - 64 n^{2} - 8 (8 n^{2}) - 8 \cdot - 8$

Step 1.3.1.5

Multiply $8$ by $- 8$ .

$3 n^{2} + 1 + 64 n^{4} - 64 n^{2} - 64 n^{2} - 8 \cdot - 8$

Step 1.3.1.6

Multiply $- 8$ by $- 8$ .

$3 n^{2} + 1 + 64 n^{4} - 64 n^{2} - 64 n^{2} + 64$

Step 1.3.2

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

$3 n^{2} + 1 + 64 n^{4} - 128 n^{2} + 64$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $128 n^{2}$ from $3 n^{2}$ .

$- 125 n^{2} + 1 + 64 n^{4} + 64$

Step 2.2

Simplify the expression.

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Step 2.2.1

Add $1$ and $64$ .

$- 125 n^{2} + 64 n^{4} + 65$

Step 2.2.2

Reorder $- 125 n^{2}$ and $64 n^{4}$ .

$64 n^{4} - 125 n^{2} + 65$