Simplify (7+3y)(3y-7)

$(7 + 3 y) (3 y - 7)$

Step 1

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

Apply the distributive property.

$7 (3 y - 7) + 3 y (3 y - 7)$

Apply the distributive property.

$7 (3 y) + 7 \cdot - 7 + 3 y (3 y - 7)$

Apply the distributive property.

$7 (3 y) + 7 \cdot - 7 + 3 y (3 y) + 3 y \cdot - 7$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $3$ by $7$ .

$21 y + 7 \cdot - 7 + 3 y (3 y) + 3 y \cdot - 7$

Multiply $7$ by $- 7$ .

$21 y - 49 + 3 y (3 y) + 3 y \cdot - 7$

Rewrite using the commutative property of multiplication.

$21 y - 49 + 3 \cdot 3 y \cdot y + 3 y \cdot - 7$

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

Move $y$ .

$21 y - 49 + 3 \cdot 3 (y \cdot y) + 3 y \cdot - 7$

Multiply $y$ by $y$ .

$21 y - 49 + 3 \cdot 3 y^{2} + 3 y \cdot - 7$

Multiply $3$ by $3$ .

$21 y - 49 + 9 y^{2} + 3 y \cdot - 7$

Multiply $- 7$ by $3$ .

$21 y - 49 + 9 y^{2} - 21 y$

Subtract $21 y$ from $21 y$ .

$- 49 + 9 y^{2} + 0$

Add $- 49$ and $0$ .

$9 y^{2} - 49$