Expand the Trigonometric Expression (-1+2p)(3-4p)

$(- 1 + 2 p) (3 - 4 p)$

Step 1

Expand $(- 1 + 2 p) (3 - 4 p)$ using the FOIL Method.

Apply the distributive property.

$- 1 (3 - 4 p) + 2 p (3 - 4 p)$

Apply the distributive property.

$- 1 \cdot 3 - 1 (- 4 p) + 2 p (3 - 4 p)$

Apply the distributive property.

$- 1 \cdot 3 - 1 (- 4 p) + 2 p \cdot 3 + 2 p (- 4 p)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $- 1$ by $3$ .

$- 3 - 1 (- 4 p) + 2 p \cdot 3 + 2 p (- 4 p)$

Multiply $- 4$ by $- 1$ .

$- 3 + 4 p + 2 p \cdot 3 + 2 p (- 4 p)$

Multiply $3$ by $2$ .

$- 3 + 4 p + 6 p + 2 p (- 4 p)$

Rewrite using the commutative property of multiplication.

$- 3 + 4 p + 6 p + 2 \cdot - 4 p \cdot p$

Multiply $p$ by $p$ by adding the exponents.

Move $p$ .

$- 3 + 4 p + 6 p + 2 \cdot - 4 (p \cdot p)$

Multiply $p$ by $p$ .

$- 3 + 4 p + 6 p + 2 \cdot - 4 p^{2}$

Multiply $2$ by $- 4$ .

$- 3 + 4 p + 6 p - 8 p^{2}$

Add $4 p$ and $6 p$ .

$- 3 + 10 p - 8 p^{2}$