Simplify (y^2-3y+4)(5y-3)

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

Step 1

Expand $(y^{2} - 3 y + 4) (5 y - 3)$ by multiplying each term in the first expression by each term in the second expression.

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

Step 2

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $y$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Move $- 3$ to the left of $y^{2}$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $y$ .

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

Multiply $y$ by $y$ .

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

Multiply $- 3$ by $5$ .

$5 y^{3} - 3 y^{2} - 15 y^{2} - 3 y \cdot - 3 + 4 (5 y) + 4 \cdot - 3$

Multiply $- 3$ by $- 3$ .

$5 y^{3} - 3 y^{2} - 15 y^{2} + 9 y + 4 (5 y) + 4 \cdot - 3$

Multiply $5$ by $4$ .

$5 y^{3} - 3 y^{2} - 15 y^{2} + 9 y + 20 y + 4 \cdot - 3$

Multiply $4$ by $- 3$ .

$5 y^{3} - 3 y^{2} - 15 y^{2} + 9 y + 20 y - 12$

Simplify by adding terms.

Subtract $15 y^{2}$ from $- 3 y^{2}$ .

$5 y^{3} - 18 y^{2} + 9 y + 20 y - 12$

Add $9 y$ and $20 y$ .

$5 y^{3} - 18 y^{2} + 29 y - 12$