Algebra Examples

$(w^{2} + 5) (w^{4} - 5 w^{2} + 25)$

Step 1

Expand $(w^{2} + 5) (w^{4} - 5 w^{2} + 25)$ by multiplying each term in the first expression by each term in the second expression.

$w^{2} w^{4} + w^{2} (- 5 w^{2}) + w^{2} \cdot 25 + 5 w^{4} + 5 (- 5 w^{2}) + 5 \cdot 25$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $w^{2}$ by $w^{4}$ by adding the exponents.

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Step 2.1.1.1

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

$w^{2 + 4} + w^{2} (- 5 w^{2}) + w^{2} \cdot 25 + 5 w^{4} + 5 (- 5 w^{2}) + 5 \cdot 25$

Step 2.1.1.2

Add $2$ and $4$ .

$w^{6} + w^{2} (- 5 w^{2}) + w^{2} \cdot 25 + 5 w^{4} + 5 (- 5 w^{2}) + 5 \cdot 25$

Step 2.1.2

Rewrite using the commutative property of multiplication.

$w^{6} - 5 w^{2} w^{2} + w^{2} \cdot 25 + 5 w^{4} + 5 (- 5 w^{2}) + 5 \cdot 25$

Step 2.1.3

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

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Step 2.1.3.1

Move $w^{2}$ .

$w^{6} - 5 (w^{2} w^{2}) + w^{2} \cdot 25 + 5 w^{4} + 5 (- 5 w^{2}) + 5 \cdot 25$

Step 2.1.3.2

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

$w^{6} - 5 w^{2 + 2} + w^{2} \cdot 25 + 5 w^{4} + 5 (- 5 w^{2}) + 5 \cdot 25$

Step 2.1.3.3

Add $2$ and $2$ .

$w^{6} - 5 w^{4} + w^{2} \cdot 25 + 5 w^{4} + 5 (- 5 w^{2}) + 5 \cdot 25$

Step 2.1.4

Move $25$ to the left of $w^{2}$ .

$w^{6} - 5 w^{4} + 25 \cdot w^{2} + 5 w^{4} + 5 (- 5 w^{2}) + 5 \cdot 25$

Step 2.1.5

Multiply $- 5$ by $5$ .

$w^{6} - 5 w^{4} + 25 w^{2} + 5 w^{4} - 25 w^{2} + 5 \cdot 25$

Step 2.1.6

Multiply $5$ by $25$ .

$w^{6} - 5 w^{4} + 25 w^{2} + 5 w^{4} - 25 w^{2} + 125$

Step 2.2

Combine the opposite terms in $w^{6} - 5 w^{4} + 25 w^{2} + 5 w^{4} - 25 w^{2} + 125$ .

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Step 2.2.1

Add $- 5 w^{4}$ and $5 w^{4}$ .

$w^{6} + 25 w^{2} + 0 - 25 w^{2} + 125$

Step 2.2.2

Add $w^{6} + 25 w^{2}$ and $0$ .

$w^{6} + 25 w^{2} - 25 w^{2} + 125$

Step 2.2.3

Subtract $25 w^{2}$ from $25 w^{2}$ .

$w^{6} + 0 + 125$

Step 2.2.4

Add $w^{6}$ and $0$ .

$w^{6} + 125$