Expand the Trigonometric Expression (6f-7)(8f-9)

$(6 f - 7) (8 f - 9)$

Step 1

Expand $(6 f - 7) (8 f - 9)$ using the FOIL Method.

Apply the distributive property.

$6 f (8 f - 9) - 7 (8 f - 9)$

Apply the distributive property.

$6 f (8 f) + 6 f \cdot - 9 - 7 (8 f - 9)$

Apply the distributive property.

$6 f (8 f) + 6 f \cdot - 9 - 7 (8 f) - 7 \cdot - 9$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$6 \cdot 8 f \cdot f + 6 f \cdot - 9 - 7 (8 f) - 7 \cdot - 9$

Multiply $f$ by $f$ by adding the exponents.

Move $f$ .

$6 \cdot 8 (f \cdot f) + 6 f \cdot - 9 - 7 (8 f) - 7 \cdot - 9$

Multiply $f$ by $f$ .

$6 \cdot 8 f^{2} + 6 f \cdot - 9 - 7 (8 f) - 7 \cdot - 9$

Multiply $6$ by $8$ .

$48 f^{2} + 6 f \cdot - 9 - 7 (8 f) - 7 \cdot - 9$

Multiply $- 9$ by $6$ .

$48 f^{2} - 54 f - 7 (8 f) - 7 \cdot - 9$

Multiply $8$ by $- 7$ .

$48 f^{2} - 54 f - 56 f - 7 \cdot - 9$

Multiply $- 7$ by $- 9$ .

$48 f^{2} - 54 f - 56 f + 63$

Subtract $56 f$ from $- 54 f$ .

$48 f^{2} - 110 f + 63$