Simplify (3p-1)(9p^2+3p+1)

$(3 p - 1) (9 p^{2} + 3 p + 1)$

Step 1

Expand $(3 p - 1) (9 p^{2} + 3 p + 1)$ by multiplying each term in the first expression by each term in the second expression.

$3 p (9 p^{2}) + 3 p (3 p) + 3 p \cdot 1 - 1 (9 p^{2}) - 1 (3 p) - 1 \cdot 1$

Step 2

Simplify terms.

Combine the opposite terms in $3 p (9 p^{2}) + 3 p (3 p) + 3 p \cdot 1 - 1 (9 p^{2}) - 1 (3 p) - 1 \cdot 1$ .

Reorder the factors in the terms $3 p \cdot 1$ and $- 1 (3 p)$ .

$3 p (9 p^{2}) + 3 p (3 p) + 1 \cdot 3 p - 1 (9 p^{2}) - 1 \cdot 3 p - 1 \cdot 1$

Subtract $3 p$ from $1 \cdot 3 p$ .

$3 p (9 p^{2}) + 3 p (3 p) - 1 (9 p^{2}) + 0 - 1 \cdot 1$

Add $3 p (9 p^{2}) + 3 p (3 p) - 1 (9 p^{2})$ and $0$ .

$3 p (9 p^{2}) + 3 p (3 p) - 1 (9 p^{2}) - 1 \cdot 1$

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 \cdot 9 p \cdot p^{2} + 3 p (3 p) - 1 (9 p^{2}) - 1 \cdot 1$

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

Move $p^{2}$ .

$3 \cdot 9 (p^{2} p) + 3 p (3 p) - 1 (9 p^{2}) - 1 \cdot 1$

Multiply $p^{2}$ by $p$ .

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

$3 \cdot 9 (p^{2} p^{1}) + 3 p (3 p) - 1 (9 p^{2}) - 1 \cdot 1$

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

$3 \cdot 9 p^{2 + 1} + 3 p (3 p) - 1 (9 p^{2}) - 1 \cdot 1$

Add $2$ and $1$ .

$3 \cdot 9 p^{3} + 3 p (3 p) - 1 (9 p^{2}) - 1 \cdot 1$

Multiply $3$ by $9$ .

$27 p^{3} + 3 p (3 p) - 1 (9 p^{2}) - 1 \cdot 1$

Rewrite using the commutative property of multiplication.

$27 p^{3} + 3 \cdot 3 p \cdot p - 1 (9 p^{2}) - 1 \cdot 1$

Multiply $p$ by $p$ by adding the exponents.

Move $p$ .

$27 p^{3} + 3 \cdot 3 (p \cdot p) - 1 (9 p^{2}) - 1 \cdot 1$

Multiply $p$ by $p$ .

$27 p^{3} + 3 \cdot 3 p^{2} - 1 (9 p^{2}) - 1 \cdot 1$

Multiply $3$ by $3$ .

$27 p^{3} + 9 p^{2} - 1 (9 p^{2}) - 1 \cdot 1$

Multiply $9$ by $- 1$ .

$27 p^{3} + 9 p^{2} - 9 p^{2} - 1 \cdot 1$

Multiply $- 1$ by $1$ .

$27 p^{3} + 9 p^{2} - 9 p^{2} - 1$

Combine the opposite terms in $27 p^{3} + 9 p^{2} - 9 p^{2} - 1$ .

Subtract $9 p^{2}$ from $9 p^{2}$ .

$27 p^{3} + 0 - 1$

Add $27 p^{3}$ and $0$ .

$27 p^{3} - 1$

Simplify (3p-1)(9p^2+3p+1)

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