Simplify (3x+5)(4x-1)

$(3 x + 5) (4 x - 1)$

Step 1

Expand $(3 x + 5) (4 x - 1)$ using the FOIL Method.

Apply the distributive property.

$3 x (4 x - 1) + 5 (4 x - 1)$

Apply the distributive property.

$3 x (4 x) + 3 x \cdot - 1 + 5 (4 x - 1)$

Apply the distributive property.

$3 x (4 x) + 3 x \cdot - 1 + 5 (4 x) + 5 \cdot - 1$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 \cdot 4 x \cdot x + 3 x \cdot - 1 + 5 (4 x) + 5 \cdot - 1$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$3 \cdot 4 (x \cdot x) + 3 x \cdot - 1 + 5 (4 x) + 5 \cdot - 1$

Multiply $x$ by $x$ .

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

Multiply $3$ by $4$ .

$12 x^{2} + 3 x \cdot - 1 + 5 (4 x) + 5 \cdot - 1$

Multiply $- 1$ by $3$ .

$12 x^{2} - 3 x + 5 (4 x) + 5 \cdot - 1$

Multiply $4$ by $5$ .

$12 x^{2} - 3 x + 20 x + 5 \cdot - 1$

Multiply $5$ by $- 1$ .

$12 x^{2} - 3 x + 20 x - 5$

Add $- 3 x$ and $20 x$ .

$12 x^{2} + 17 x - 5$