Simplify (3x-5)(2x+7)

$(3 x - 5) (2 x + 7)$

Step 1

Expand $(3 x - 5) (2 x + 7)$ using the FOIL Method.

Apply the distributive property.

$3 x (2 x + 7) - 5 (2 x + 7)$

Apply the distributive property.

$3 x (2 x) + 3 x \cdot 7 - 5 (2 x + 7)$

Apply the distributive property.

$3 x (2 x) + 3 x \cdot 7 - 5 (2 x) - 5 \cdot 7$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 \cdot 2 x \cdot x + 3 x \cdot 7 - 5 (2 x) - 5 \cdot 7$

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

Move $x$ .

$3 \cdot 2 (x \cdot x) + 3 x \cdot 7 - 5 (2 x) - 5 \cdot 7$

Multiply $x$ by $x$ .

$3 \cdot 2 x^{2} + 3 x \cdot 7 - 5 (2 x) - 5 \cdot 7$

Multiply $3$ by $2$ .

$6 x^{2} + 3 x \cdot 7 - 5 (2 x) - 5 \cdot 7$

Multiply $7$ by $3$ .

$6 x^{2} + 21 x - 5 (2 x) - 5 \cdot 7$

Multiply $2$ by $- 5$ .

$6 x^{2} + 21 x - 10 x - 5 \cdot 7$

Multiply $- 5$ by $7$ .

$6 x^{2} + 21 x - 10 x - 35$

Subtract $10 x$ from $21 x$ .

$6 x^{2} + 11 x - 35$