Simplify -10(r+1)-5r(1-5r)

$- 10 (r + 1) - 5 r (1 - 5 r)$

Step 1

Simplify each term.

Apply the distributive property.

$- 10 r - 10 \cdot 1 - 5 r (1 - 5 r)$

Multiply $- 10$ by $1$ .

$- 10 r - 10 - 5 r (1 - 5 r)$

Apply the distributive property.

$- 10 r - 10 - 5 r \cdot 1 - 5 r (- 5 r)$

Multiply $- 5$ by $1$ .

$- 10 r - 10 - 5 r - 5 r (- 5 r)$

Rewrite using the commutative property of multiplication.

$- 10 r - 10 - 5 r - 5 \cdot - 5 r \cdot r$

Simplify each term.

Multiply $r$ by $r$ by adding the exponents.

Move $r$ .

$- 10 r - 10 - 5 r - 5 \cdot - 5 (r \cdot r)$

Multiply $r$ by $r$ .

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

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

Multiply $- 5$ by $- 5$ .

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

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

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

Step 2

Simplify by adding terms.

Subtract $5 r$ from $- 10 r$ .

$- 15 r - 10 + 25 r^{2}$

Simplify the expression.

Move $- 10$ .

$- 15 r + 25 r^{2} - 10$

Reorder $- 15 r$ and $25 r^{2}$ .

$25 r^{2} - 15 r - 10$

$25 r^{2} - 15 r - 10$

$25 r^{2} - 15 r - 10$

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