Expand the Trigonometric Expression (1-5z)(2-5z)

$(1 - 5 z) (2 - 5 z)$

Step 1

Expand $(1 - 5 z) (2 - 5 z)$ using the FOIL Method.

Apply the distributive property.

$1 (2 - 5 z) - 5 z (2 - 5 z)$

Apply the distributive property.

$1 \cdot 2 + 1 (- 5 z) - 5 z (2 - 5 z)$

Apply the distributive property.

$1 \cdot 2 + 1 (- 5 z) - 5 z \cdot 2 - 5 z (- 5 z)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $2$ by $1$ .

$2 + 1 (- 5 z) - 5 z \cdot 2 - 5 z (- 5 z)$

Multiply $- 5 z$ by $1$ .

$2 - 5 z - 5 z \cdot 2 - 5 z (- 5 z)$

Multiply $2$ by $- 5$ .

$2 - 5 z - 10 z - 5 z (- 5 z)$

Rewrite using the commutative property of multiplication.

$2 - 5 z - 10 z - 5 \cdot - 5 z \cdot z$

Multiply $z$ by $z$ by adding the exponents.

Move $z$ .

$2 - 5 z - 10 z - 5 \cdot - 5 (z \cdot z)$

Multiply $z$ by $z$ .

$2 - 5 z - 10 z - 5 \cdot - 5 z^{2}$

Multiply $- 5$ by $- 5$ .

$2 - 5 z - 10 z + 25 z^{2}$

Subtract $10 z$ from $- 5 z$ .

$2 - 15 z + 25 z^{2}$