Algebra Examples

- p^{2} (p^{2} - p - 1)

$- p^{2} (p^{2} - p - 1)$

Step 1

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

a x^{2} + b x + c

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

Step 2

Apply the distributive property.

- p^{2} p^{2} - p^{2} (- p) - p^{2} \cdot - 1

$- p^{2} p^{2} - p^{2} (- p) - p^{2} \cdot - 1$

Step 3

Simplify.

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Step 3.1

Multiply

p^{2}

$p^{2}$ by

p^{2}

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

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Step 3.1.1

Move

p^{2}

$p^{2}$ .

- (p^{2} p^{2}) - p^{2} (- p) - p^{2} \cdot - 1

$- (p^{2} p^{2}) - p^{2} (- p) - p^{2} \cdot - 1$

Step 3.1.2

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} (- p) - p^{2} \cdot - 1

$- p^{2 + 2} - p^{2} (- p) - p^{2} \cdot - 1$

Step 3.1.3

Add

2

$2$ and

2

$2$ .

- p^{4} - p^{2} (- p) - p^{2} \cdot - 1

$- p^{4} - p^{2} (- p) - p^{2} \cdot - 1$

- p^{4} - p^{2} (- p) - p^{2} \cdot - 1

$- p^{4} - p^{2} (- p) - p^{2} \cdot - 1$

Step 3.2

Rewrite using the commutative property of multiplication.

- p^{4} - 1 \cdot - 1 p^{2} p - p^{2} \cdot - 1

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

Step 3.3

Multiply

- p^{2} \cdot - 1

$- p^{2} \cdot - 1$ .

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Step 3.3.1

Multiply

- 1

$- 1$ by

- 1

$- 1$ .

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

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

Step 3.3.2

Multiply

p^{2}

$p^{2}$ by

1

$1$ .

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

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

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

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

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

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

Step 4

Simplify each term.

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Step 4.1

Multiply

p^{2}

$p^{2}$ by

p

$p$ by adding the exponents.

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Step 4.1.1

Move

p

$p$ .

- p^{4} - 1 \cdot - 1 (p \cdot p^{2}) + p^{2}

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

Step 4.1.2

Multiply

p

$p$ by

p^{2}

$p^{2}$ .

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Step 4.1.2.1

Raise

p

$p$ to the power of

1

$1$ .

- p^{4} - 1 \cdot - 1 (p^{1} p^{2}) + p^{2}

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

Step 4.1.2.2

Use the power rule

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

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

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

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

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

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

Step 4.1.3

Add

1

$1$ and

2

$2$ .

- p^{4} - 1 \cdot - 1 p^{3} + p^{2}

$- p^{4} - 1 \cdot - 1 p^{3} + p^{2}$

- p^{4} - 1 \cdot - 1 p^{3} + p^{2}

$- p^{4} - 1 \cdot - 1 p^{3} + p^{2}$

Step 4.2

Multiply

- 1

$- 1$ by

- 1

$- 1$ .

- p^{4} + 1 p^{3} + p^{2}

$- p^{4} + 1 p^{3} + p^{2}$

Step 4.3

Multiply

p^{3}

$p^{3}$ by

1

$1$ .

- p^{4} + p^{3} + p^{2}

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

- p^{4} + p^{3} + p^{2}

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

- p^{2} (p^{2} - p - 1)

$- p^{2} (p^{2} - p - 1)$

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[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$