Simplify (7y-4)(2y+3)-13y

$(7 y - 4) (2 y + 3) - 13 y$

Step 1

Simplify each term.

Expand $(7 y - 4) (2 y + 3)$ using the FOIL Method.

Apply the distributive property.

$7 y (2 y + 3) - 4 (2 y + 3) - 13 y$

Apply the distributive property.

$7 y (2 y) + 7 y \cdot 3 - 4 (2 y + 3) - 13 y$

Apply the distributive property.

$7 y (2 y) + 7 y \cdot 3 - 4 (2 y) - 4 \cdot 3 - 13 y$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$7 \cdot 2 y \cdot y + 7 y \cdot 3 - 4 (2 y) - 4 \cdot 3 - 13 y$

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

Move $y$ .

$7 \cdot 2 (y \cdot y) + 7 y \cdot 3 - 4 (2 y) - 4 \cdot 3 - 13 y$

Multiply $y$ by $y$ .

$7 \cdot 2 y^{2} + 7 y \cdot 3 - 4 (2 y) - 4 \cdot 3 - 13 y$

Multiply $7$ by $2$ .

$14 y^{2} + 7 y \cdot 3 - 4 (2 y) - 4 \cdot 3 - 13 y$

Multiply $3$ by $7$ .

$14 y^{2} + 21 y - 4 (2 y) - 4 \cdot 3 - 13 y$

Multiply $2$ by $- 4$ .

$14 y^{2} + 21 y - 8 y - 4 \cdot 3 - 13 y$

Multiply $- 4$ by $3$ .

$14 y^{2} + 21 y - 8 y - 12 - 13 y$

Subtract $8 y$ from $21 y$ .

$14 y^{2} + 13 y - 12 - 13 y$

Step 2

Combine the opposite terms in $14 y^{2} + 13 y - 12 - 13 y$ .

Subtract $13 y$ from $13 y$ .

$14 y^{2} + 0 - 12$

Add $14 y^{2}$ and $0$ .

$14 y^{2} - 12$