Expand the Trigonometric Expression (7x+5)(2x-3)

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $7$ by $2$ .

$14 x^{2} + 7 x \cdot - 3 + 5 (2 x) + 5 \cdot - 3$

Multiply $- 3$ by $7$ .

$14 x^{2} - 21 x + 5 (2 x) + 5 \cdot - 3$

Multiply $2$ by $5$ .

$14 x^{2} - 21 x + 10 x + 5 \cdot - 3$

Multiply $5$ by $- 3$ .

$14 x^{2} - 21 x + 10 x - 15$

Add $- 21 x$ and $10 x$ .

$14 x^{2} - 11 x - 15$