Find the Product (-3y+1)(4y^2-y-7)

$(- 3 y + 1) (4 y^{2} - y - 7)$

Expand $(- 3 y + 1) (4 y^{2} - y - 7)$ by multiplying each term in the first expression by each term in the second expression.

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

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $y^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Multiply $- 3$ by $4$ .

$- 12 y^{3} - 3 y (- y) - 3 y \cdot - 7 + 1 (4 y^{2}) + 1 (- y) + 1 \cdot - 7$

Rewrite using the commutative property of multiplication.

$- 12 y^{3} - 3 \cdot - 1 y \cdot y - 3 y \cdot - 7 + 1 (4 y^{2}) + 1 (- y) + 1 \cdot - 7$

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$- 12 y^{3} - 3 \cdot - 1 (y \cdot y) - 3 y \cdot - 7 + 1 (4 y^{2}) + 1 (- y) + 1 \cdot - 7$

Multiply $y$ by $y$ .

$- 12 y^{3} - 3 \cdot - 1 y^{2} - 3 y \cdot - 7 + 1 (4 y^{2}) + 1 (- y) + 1 \cdot - 7$

Multiply $- 3$ by $- 1$ .

$- 12 y^{3} + 3 y^{2} - 3 y \cdot - 7 + 1 (4 y^{2}) + 1 (- y) + 1 \cdot - 7$

Multiply $- 7$ by $- 3$ .

$- 12 y^{3} + 3 y^{2} + 21 y + 1 (4 y^{2}) + 1 (- y) + 1 \cdot - 7$

Multiply $4 y^{2}$ by $1$ .

$- 12 y^{3} + 3 y^{2} + 21 y + 4 y^{2} + 1 (- y) + 1 \cdot - 7$

Multiply $- y$ by $1$ .

$- 12 y^{3} + 3 y^{2} + 21 y + 4 y^{2} - y + 1 \cdot - 7$

Multiply $- 7$ by $1$ .

$- 12 y^{3} + 3 y^{2} + 21 y + 4 y^{2} - y - 7$

Simplify by adding terms.

Add $3 y^{2}$ and $4 y^{2}$ .

$- 12 y^{3} + 7 y^{2} + 21 y - y - 7$

Subtract $y$ from $21 y$ .

$- 12 y^{3} + 7 y^{2} + 20 y - 7$