Algebra Examples

(p^{2} + p - 6) (p^{2} - 6)

$(p^{2} + p - 6) (p^{2} - 6)$

Step 1

Expand

(p^{2} + p - 6) (p^{2} - 6)

$(p^{2} + p - 6) (p^{2} - 6)$ by multiplying each term in the first expression by each term in the second expression.

p^{2} p^{2} + p^{2} \cdot - 6 + p \cdot p^{2} + p \cdot - 6 - 6 p^{2} - 6 \cdot - 6

$p^{2} p^{2} + p^{2} \cdot - 6 + p \cdot p^{2} + p \cdot - 6 - 6 p^{2} - 6 \cdot - 6$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply

p^{2}

$p^{2}$ by

p^{2}

$p^{2}$ by adding the exponents.

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Step 2.1.1.1

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

p^{2 + 2} + p^{2} \cdot - 6 + p \cdot p^{2} + p \cdot - 6 - 6 p^{2} - 6 \cdot - 6

$p^{2 + 2} + p^{2} \cdot - 6 + p \cdot p^{2} + p \cdot - 6 - 6 p^{2} - 6 \cdot - 6$

Step 2.1.1.2

Add

2

$2$ and

2

$2$ .

p^{4} + p^{2} \cdot - 6 + p \cdot p^{2} + p \cdot - 6 - 6 p^{2} - 6 \cdot - 6

$p^{4} + p^{2} \cdot - 6 + p \cdot p^{2} + p \cdot - 6 - 6 p^{2} - 6 \cdot - 6$

Step 2.1.2

Move

$- 6$ to the left of

$p^{2}$ .

$p^{4} - 6 \cdot p^{2} + p \cdot p^{2} + p \cdot - 6 - 6 p^{2} - 6 \cdot - 6$

Step 2.1.3

Multiply

$p$ by

$p^{2}$ by adding the exponents.

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Step 2.1.3.1

Multiply

$p$ by

$p^{2}$ .

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Step 2.1.3.1.1

Raise

$p$ to the power of

$1$ .

$p^{4} - 6 p^{2} + p^{1} p^{2} + p \cdot - 6 - 6 p^{2} - 6 \cdot - 6$

Step 2.1.3.1.2

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$p^{4} - 6 p^{2} + p^{1 + 2} + p \cdot - 6 - 6 p^{2} - 6 \cdot - 6$

Step 2.1.3.2

Add

$1$ and

$2$ .

$p^{4} - 6 p^{2} + p^{3} + p \cdot - 6 - 6 p^{2} - 6 \cdot - 6$

Step 2.1.4

Move

$- 6$ to the left of

$p$ .

$p^{4} - 6 p^{2} + p^{3} - 6 \cdot p - 6 p^{2} - 6 \cdot - 6$

Step 2.1.5

Multiply

$- 6$ by

$- 6$ .

$p^{4} - 6 p^{2} + p^{3} - 6 p - 6 p^{2} + 36$

Step 2.2

Subtract

$6 p^{2}$ from

$- 6 p^{2}$ .

$p^{4} - 12 p^{2} + p^{3} - 6 p + 36$