Simplify (3y+7)(4y+5)

$(3 y + 7) (4 y + 5)$

Step 1

Expand $(3 y + 7) (4 y + 5)$ using the FOIL Method.

Apply the distributive property.

$3 y (4 y + 5) + 7 (4 y + 5)$

Apply the distributive property.

$3 y (4 y) + 3 y \cdot 5 + 7 (4 y + 5)$

Apply the distributive property.

$3 y (4 y) + 3 y \cdot 5 + 7 (4 y) + 7 \cdot 5$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 \cdot 4 y \cdot y + 3 y \cdot 5 + 7 (4 y) + 7 \cdot 5$

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

Move $y$ .

$3 \cdot 4 (y \cdot y) + 3 y \cdot 5 + 7 (4 y) + 7 \cdot 5$

Multiply $y$ by $y$ .

$3 \cdot 4 y^{2} + 3 y \cdot 5 + 7 (4 y) + 7 \cdot 5$

Multiply $3$ by $4$ .

$12 y^{2} + 3 y \cdot 5 + 7 (4 y) + 7 \cdot 5$

Multiply $5$ by $3$ .

$12 y^{2} + 15 y + 7 (4 y) + 7 \cdot 5$

Multiply $4$ by $7$ .

$12 y^{2} + 15 y + 28 y + 7 \cdot 5$

Multiply $7$ by $5$ .

$12 y^{2} + 15 y + 28 y + 35$

Add $15 y$ and $28 y$ .

$12 y^{2} + 43 y + 35$