Solve -{2x^2-[x(x+2y)+3xy-w(1-w)]+4w^2}

$$- \{ 2 x ^ { 2 } - [ x ( x + 2 y ) + 3 x y - w ( 1 - w ) ] + 4 w ^ { 2 } \}$$

Evaluate

$$-x^{2}+5xy-3w^{2}-w$$

Solution Steps

Use the distributive property to multiply x by x+2y.

$$-\left(2x^{2}-\left(x^{2}+2xy+3xy-w\left(1-w\right)\right)+4w^{2}\right)$$

Combine 2xy and 3xy to get 5xy.

$$-\left(2x^{2}-\left(x^{2}+5xy-w\left(1-w\right)\right)+4w^{2}\right)$$

Use the distributive property to multiply w by 1-w.

$$-\left(2x^{2}-\left(x^{2}+5xy-\left(w-w^{2}\right)\right)+4w^{2}\right)$$

To find the opposite of w-w^{2}, find the opposite of each term.

$$-\left(2x^{2}-\left(x^{2}+5xy-w+w^{2}\right)+4w^{2}\right)$$

To find the opposite of x^{2}+5xy-w+w^{2}, find the opposite of each term.

$$-\left(2x^{2}-x^{2}-5xy+w-w^{2}+4w^{2}\right)$$

Combine 2x^{2} and -x^{2} to get x^{2}.

$$-\left(x^{2}-5xy+w-w^{2}+4w^{2}\right)$$

Combine -w^{2} and 4w^{2} to get 3w^{2}.

$$-\left(x^{2}-5xy+w+3w^{2}\right)$$

To find the opposite of x^{2}-5xy+w+3w^{2}, find the opposite of each term.

$$-x^{2}+5xy-w-3w^{2}$$

Expand

$$-x^{2}+5xy-3w^{2}-w$$

Solution Steps

Use the distributive property to multiply x by x+2y.

$$-\left(2x^{2}-\left(x^{2}+2xy+3xy-w\left(1-w\right)\right)+4w^{2}\right)$$

Combine 2xy and 3xy to get 5xy.

$$-\left(2x^{2}-\left(x^{2}+5xy-w\left(1-w\right)\right)+4w^{2}\right)$$

Use the distributive property to multiply w by 1-w.

$$-\left(2x^{2}-\left(x^{2}+5xy-\left(w-w^{2}\right)\right)+4w^{2}\right)$$

To find the opposite of w-w^{2}, find the opposite of each term.

$$-\left(2x^{2}-\left(x^{2}+5xy-w+w^{2}\right)+4w^{2}\right)$$

To find the opposite of x^{2}+5xy-w+w^{2}, find the opposite of each term.

$$-\left(2x^{2}-x^{2}-5xy+w-w^{2}+4w^{2}\right)$$

Combine 2x^{2} and -x^{2} to get x^{2}.

$$-\left(x^{2}-5xy+w-w^{2}+4w^{2}\right)$$

Combine -w^{2} and 4w^{2} to get 3w^{2}.

$$-\left(x^{2}-5xy+w+3w^{2}\right)$$

To find the opposite of x^{2}-5xy+w+3w^{2}, find the opposite of each term.

$$-x^{2}+5xy-w-3w^{2}$$