Algebra Examples

${(3 - 8 w^{2})}^{2}$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Rewrite ${(3 - 8 w^{2})}^{2}$ as $(3 - 8 w^{2}) (3 - 8 w^{2})$ .

$(3 - 8 w^{2}) (3 - 8 w^{2})$

Step 3

Expand $(3 - 8 w^{2}) (3 - 8 w^{2})$ using the FOIL Method.

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Step 3.1

Apply the distributive property.

$3 (3 - 8 w^{2}) - 8 w^{2} (3 - 8 w^{2})$

Step 3.2

Apply the distributive property.

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

Step 3.3

Apply the distributive property.

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

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 $3$ by $3$ .

$9 + 3 (- 8 w^{2}) - 8 w^{2} \cdot 3 - 8 w^{2} (- 8 w^{2})$

Step 4.1.2

Multiply $- 8$ by $3$ .

$9 - 24 w^{2} - 8 w^{2} \cdot 3 - 8 w^{2} (- 8 w^{2})$

Step 4.1.3

Multiply $3$ by $- 8$ .

$9 - 24 w^{2} - 24 w^{2} - 8 w^{2} (- 8 w^{2})$

Step 4.1.4

Rewrite using the commutative property of multiplication.

$9 - 24 w^{2} - 24 w^{2} - 8 \cdot - 8 w^{2} w^{2}$

Step 4.1.5

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

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Step 4.1.5.1

Move $w^{2}$ .

$9 - 24 w^{2} - 24 w^{2} - 8 \cdot - 8 (w^{2} w^{2})$

Step 4.1.5.2

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

$9 - 24 w^{2} - 24 w^{2} - 8 \cdot - 8 w^{2 + 2}$

Step 4.1.5.3

Add $2$ and $2$ .

$9 - 24 w^{2} - 24 w^{2} - 8 \cdot - 8 w^{4}$

Step 4.1.6

Multiply $- 8$ by $- 8$ .

$9 - 24 w^{2} - 24 w^{2} + 64 w^{4}$

Step 4.2

Subtract $24 w^{2}$ from $- 24 w^{2}$ .

$9 - 48 w^{2} + 64 w^{4}$

Step 5

Move $9$ .

$- 48 w^{2} + 64 w^{4} + 9$

Step 6

Reorder $- 48 w^{2}$ and $64 w^{4}$ .

$64 w^{4} - 48 w^{2} + 9$