Expand the Trigonometric Expression (p^3)(2p^2-4p)(3p^2-1)

$(p^{3}) (2 p^{2} - 4 p) (3 p^{2} - 1)$

Step 1

Simplify terms.

Apply the distributive property.

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

Reorder.

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

$(2 p^{3} p^{2} - 4 p^{3} p) (3 p^{2} - 1)$

Simplify each term.

Multiply $p^{3}$ by $p^{2}$ by adding the exponents.

Move $p^{2}$ .

$(2 (p^{2} p^{3}) - 4 p^{3} p) (3 p^{2} - 1)$

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

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

Add $2$ and $3$ .

$(2 p^{5} - 4 p^{3} p) (3 p^{2} - 1)$

Multiply $p^{3}$ by $p$ by adding the exponents.

Move $p$ .

$(2 p^{5} - 4 (p \cdot p^{3})) (3 p^{2} - 1)$

Multiply $p$ by $p^{3}$ .

Raise $p$ to the power of $1$ .

$(2 p^{5} - 4 (p^{1} p^{3})) (3 p^{2} - 1)$

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

$(2 p^{5} - 4 p^{1 + 3}) (3 p^{2} - 1)$

Add $1$ and $3$ .

$(2 p^{5} - 4 p^{4}) (3 p^{2} - 1)$

Step 2

Expand $(2 p^{5} - 4 p^{4}) (3 p^{2} - 1)$ using the FOIL Method.

Apply the distributive property.

$2 p^{5} (3 p^{2} - 1) - 4 p^{4} (3 p^{2} - 1)$

Apply the distributive property.

$2 p^{5} (3 p^{2}) + 2 p^{5} \cdot - 1 - 4 p^{4} (3 p^{2} - 1)$

Apply the distributive property.

$2 p^{5} (3 p^{2}) + 2 p^{5} \cdot - 1 - 4 p^{4} (3 p^{2}) - 4 p^{4} \cdot - 1$

Step 3

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 3 p^{5} p^{2} + 2 p^{5} \cdot - 1 - 4 p^{4} (3 p^{2}) - 4 p^{4} \cdot - 1$

Multiply $p^{5}$ by $p^{2}$ by adding the exponents.

Move $p^{2}$ .

$2 \cdot 3 (p^{2} p^{5}) + 2 p^{5} \cdot - 1 - 4 p^{4} (3 p^{2}) - 4 p^{4} \cdot - 1$

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

$2 \cdot 3 p^{2 + 5} + 2 p^{5} \cdot - 1 - 4 p^{4} (3 p^{2}) - 4 p^{4} \cdot - 1$

Add $2$ and $5$ .

$2 \cdot 3 p^{7} + 2 p^{5} \cdot - 1 - 4 p^{4} (3 p^{2}) - 4 p^{4} \cdot - 1$

Multiply $2$ by $3$ .

$6 p^{7} + 2 p^{5} \cdot - 1 - 4 p^{4} (3 p^{2}) - 4 p^{4} \cdot - 1$

Multiply $- 1$ by $2$ .

$6 p^{7} - 2 p^{5} - 4 p^{4} (3 p^{2}) - 4 p^{4} \cdot - 1$

Rewrite using the commutative property of multiplication.

$6 p^{7} - 2 p^{5} - 4 \cdot 3 p^{4} p^{2} - 4 p^{4} \cdot - 1$

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

Move $p^{2}$ .

$6 p^{7} - 2 p^{5} - 4 \cdot 3 (p^{2} p^{4}) - 4 p^{4} \cdot - 1$

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

$6 p^{7} - 2 p^{5} - 4 \cdot 3 p^{2 + 4} - 4 p^{4} \cdot - 1$

Add $2$ and $4$ .

$6 p^{7} - 2 p^{5} - 4 \cdot 3 p^{6} - 4 p^{4} \cdot - 1$

Multiply $- 4$ by $3$ .

$6 p^{7} - 2 p^{5} - 12 p^{6} - 4 p^{4} \cdot - 1$

Multiply $- 1$ by $- 4$ .

$6 p^{7} - 2 p^{5} - 12 p^{6} + 4 p^{4}$

Expand the Trigonometric Expression (p^3)(2p^2-4p)(3p^2-1)

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