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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

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

Multiply $a$ by $a$ .

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

Multiply $3$ by $2$ .

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

Multiply $- 7$ by $3$ .

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

Multiply $2$ by $5$ .

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

Multiply $5$ by $- 7$ .

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

Add $- 21 a$ and $10 a$ .

$6 a^{2} - 11 a - 35$