Simplify 2(3y-7)-5y(2-y)

$2 (3 y - 7) - 5 y (2 - y)$

Step 1

Simplify each term.

Apply the distributive property.

$2 (3 y) + 2 \cdot - 7 - 5 y (2 - y)$

Multiply $3$ by $2$ .

$6 y + 2 \cdot - 7 - 5 y (2 - y)$

Multiply $2$ by $- 7$ .

$6 y - 14 - 5 y (2 - y)$

Apply the distributive property.

$6 y - 14 - 5 y \cdot 2 - 5 y (- y)$

Multiply $2$ by $- 5$ .

$6 y - 14 - 10 y - 5 y (- y)$

Rewrite using the commutative property of multiplication.

$6 y - 14 - 10 y - 5 \cdot - 1 y \cdot y$

Simplify each term.

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$6 y - 14 - 10 y - 5 \cdot - 1 (y \cdot y)$

Multiply $y$ by $y$ .

$6 y - 14 - 10 y - 5 \cdot - 1 y^{2}$

$6 y - 14 - 10 y - 5 \cdot - 1 y^{2}$

Multiply $- 5$ by $- 1$ .

$6 y - 14 - 10 y + 5 y^{2}$

$6 y - 14 - 10 y + 5 y^{2}$

$6 y - 14 - 10 y + 5 y^{2}$

Step 2

Simplify by adding terms.

Subtract $10 y$ from $6 y$ .

$- 4 y - 14 + 5 y^{2}$

Simplify the expression.

Move $- 14$ .

$- 4 y + 5 y^{2} - 14$

Reorder $- 4 y$ and $5 y^{2}$ .

$5 y^{2} - 4 y - 14$

$5 y^{2} - 4 y - 14$

$5 y^{2} - 4 y - 14$

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