Simplify (6z^2-4z+1)(8-3z)

$(6 z^{2} - 4 z + 1) (8 - 3 z)$

Step 1

Expand $(6 z^{2} - 4 z + 1) (8 - 3 z)$ by multiplying each term in the first expression by each term in the second expression.

$6 z^{2} \cdot 8 + 6 z^{2} (- 3 z) - 4 z \cdot 8 - 4 z (- 3 z) + 1 \cdot 8 + 1 (- 3 z)$

Step 2

Simplify terms.

Simplify each term.

Multiply $8$ by $6$ .

$48 z^{2} + 6 z^{2} (- 3 z) - 4 z \cdot 8 - 4 z (- 3 z) + 1 \cdot 8 + 1 (- 3 z)$

Rewrite using the commutative property of multiplication.

$48 z^{2} + 6 \cdot - 3 z^{2} z - 4 z \cdot 8 - 4 z (- 3 z) + 1 \cdot 8 + 1 (- 3 z)$

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

Move $z$ .

$48 z^{2} + 6 \cdot - 3 (z \cdot z^{2}) - 4 z \cdot 8 - 4 z (- 3 z) + 1 \cdot 8 + 1 (- 3 z)$

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

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

$48 z^{2} + 6 \cdot - 3 (z^{1} z^{2}) - 4 z \cdot 8 - 4 z (- 3 z) + 1 \cdot 8 + 1 (- 3 z)$

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

$48 z^{2} + 6 \cdot - 3 z^{1 + 2} - 4 z \cdot 8 - 4 z (- 3 z) + 1 \cdot 8 + 1 (- 3 z)$

Add $1$ and $2$ .

$48 z^{2} + 6 \cdot - 3 z^{3} - 4 z \cdot 8 - 4 z (- 3 z) + 1 \cdot 8 + 1 (- 3 z)$

Multiply $6$ by $- 3$ .

$48 z^{2} - 18 z^{3} - 4 z \cdot 8 - 4 z (- 3 z) + 1 \cdot 8 + 1 (- 3 z)$

Multiply $8$ by $- 4$ .

$48 z^{2} - 18 z^{3} - 32 z - 4 z (- 3 z) + 1 \cdot 8 + 1 (- 3 z)$

Rewrite using the commutative property of multiplication.

$48 z^{2} - 18 z^{3} - 32 z - 4 \cdot - 3 z \cdot z + 1 \cdot 8 + 1 (- 3 z)$

Multiply $z$ by $z$ by adding the exponents.

Move $z$ .

$48 z^{2} - 18 z^{3} - 32 z - 4 \cdot - 3 (z \cdot z) + 1 \cdot 8 + 1 (- 3 z)$

Multiply $z$ by $z$ .

$48 z^{2} - 18 z^{3} - 32 z - 4 \cdot - 3 z^{2} + 1 \cdot 8 + 1 (- 3 z)$

Multiply $- 4$ by $- 3$ .

$48 z^{2} - 18 z^{3} - 32 z + 12 z^{2} + 1 \cdot 8 + 1 (- 3 z)$

Multiply $8$ by $1$ .

$48 z^{2} - 18 z^{3} - 32 z + 12 z^{2} + 8 + 1 (- 3 z)$

Multiply $- 3 z$ by $1$ .

$48 z^{2} - 18 z^{3} - 32 z + 12 z^{2} + 8 - 3 z$

Simplify by adding terms.

Add $48 z^{2}$ and $12 z^{2}$ .

$60 z^{2} - 18 z^{3} - 32 z + 8 - 3 z$

Subtract $3 z$ from $- 32 z$ .

$60 z^{2} - 18 z^{3} - 35 z + 8$

Reorder $60 z^{2}$ and $- 18 z^{3}$ .

$- 18 z^{3} + 60 z^{2} - 35 z + 8$