Expand the Trigonometric Expression (-f+10)(3f-1)

$(- f + 10) (3 f - 1)$

Step 1

Expand $(- f + 10) (3 f - 1)$ using the FOIL Method.

Apply the distributive property.

$- f (3 f - 1) + 10 (3 f - 1)$

Apply the distributive property.

$- f (3 f) - f \cdot - 1 + 10 (3 f - 1)$

Apply the distributive property.

$- f (3 f) - f \cdot - 1 + 10 (3 f) + 10 \cdot - 1$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$- 1 \cdot 3 f \cdot f - f \cdot - 1 + 10 (3 f) + 10 \cdot - 1$

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

Move $f$ .

$- 1 \cdot 3 (f \cdot f) - f \cdot - 1 + 10 (3 f) + 10 \cdot - 1$

Multiply $f$ by $f$ .

$- 1 \cdot 3 f^{2} - f \cdot - 1 + 10 (3 f) + 10 \cdot - 1$

Multiply $- 1$ by $3$ .

$- 3 f^{2} - f \cdot - 1 + 10 (3 f) + 10 \cdot - 1$

Multiply $- f \cdot - 1$ .

Multiply $- 1$ by $- 1$ .

$- 3 f^{2} + 1 f + 10 (3 f) + 10 \cdot - 1$

Multiply $f$ by $1$ .

$- 3 f^{2} + f + 10 (3 f) + 10 \cdot - 1$

Multiply $3$ by $10$ .

$- 3 f^{2} + f + 30 f + 10 \cdot - 1$

Multiply $10$ by $- 1$ .

$- 3 f^{2} + f + 30 f - 10$

Add $f$ and $30 f$ .

$- 3 f^{2} + 31 f - 10$