Find the Product a^4(3a^2-2a+1)

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

Step 1

Apply the distributive property.

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

Step 2

Simplify.

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

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

Multiply $a^{4}$ by $1$ .

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

Step 3

Simplify each term.

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

Move $a^{2}$ .

$3 (a^{2} a^{4}) - 2 a^{4} a + a^{4}$

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

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

Add $2$ and $4$ .

$3 a^{6} - 2 a^{4} a + a^{4}$

Multiply $a^{4}$ by $a$ by adding the exponents.

Move $a$ .

$3 a^{6} - 2 (a \cdot a^{4}) + a^{4}$

Multiply $a$ by $a^{4}$ .

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

$3 a^{6} - 2 (a^{1} a^{4}) + a^{4}$

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

$3 a^{6} - 2 a^{1 + 4} + a^{4}$

Add $1$ and $4$ .

$3 a^{6} - 2 a^{5} + a^{4}$