Simplify (2x^2-4x+3y-6)-(4y^2-3x-7y+4)

$(2 x^{2} - 4 x + 3 y - 6) - (4 y^{2} - 3 x - 7 y + 4)$

Step 1

Simplify each term.

Apply the distributive property.

$2 x^{2} - 4 x + 3 y - 6 - (4 y^{2}) - (- 3 x) - (- 7 y) - 1 \cdot 4$

Simplify.

Multiply $4$ by $- 1$ .

$2 x^{2} - 4 x + 3 y - 6 - 4 y^{2} - (- 3 x) - (- 7 y) - 1 \cdot 4$

Multiply $- 3$ by $- 1$ .

$2 x^{2} - 4 x + 3 y - 6 - 4 y^{2} + 3 x - (- 7 y) - 1 \cdot 4$

Multiply $- 7$ by $- 1$ .

$2 x^{2} - 4 x + 3 y - 6 - 4 y^{2} + 3 x + 7 y - 1 \cdot 4$

Multiply $- 1$ by $4$ .

$2 x^{2} - 4 x + 3 y - 6 - 4 y^{2} + 3 x + 7 y - 4$

Step 2

Simplify by adding terms.

Add $- 4 x$ and $3 x$ .

$2 x^{2} - x + 3 y - 6 - 4 y^{2} + 7 y - 4$

Add $3 y$ and $7 y$ .

$2 x^{2} - x + 10 y - 6 - 4 y^{2} - 4$

Simplify the expression.

Subtract $4$ from $- 6$ .

$2 x^{2} - x + 10 y - 4 y^{2} - 10$

Move $10 y$ .

$2 x^{2} - x - 4 y^{2} + 10 y - 10$

Move $- x$ .

$2 x^{2} - 4 y^{2} - x + 10 y - 10$