Simplify (5r+2)(3r-4)

$(5 r + 2) (3 r - 4)$

Step 1

Expand $(5 r + 2) (3 r - 4)$ using the FOIL Method.

Apply the distributive property.

$5 r (3 r - 4) + 2 (3 r - 4)$

Apply the distributive property.

$5 r (3 r) + 5 r \cdot - 4 + 2 (3 r - 4)$

Apply the distributive property.

$5 r (3 r) + 5 r \cdot - 4 + 2 (3 r) + 2 \cdot - 4$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$5 \cdot 3 r \cdot r + 5 r \cdot - 4 + 2 (3 r) + 2 \cdot - 4$

Multiply $r$ by $r$ by adding the exponents.

Move $r$ .

$5 \cdot 3 (r \cdot r) + 5 r \cdot - 4 + 2 (3 r) + 2 \cdot - 4$

Multiply $r$ by $r$ .

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

Multiply $5$ by $3$ .

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

Multiply $- 4$ by $5$ .

$15 r^{2} - 20 r + 2 (3 r) + 2 \cdot - 4$

Multiply $3$ by $2$ .

$15 r^{2} - 20 r + 6 r + 2 \cdot - 4$

Multiply $2$ by $- 4$ .

$15 r^{2} - 20 r + 6 r - 8$

Add $- 20 r$ and $6 r$ .

$15 r^{2} - 14 r - 8$