Solve -w(-5w-7)-w(1-w)

$$- w ( - 5 w - 7 ) - w ( 1 - w )$$

Evaluate

$$6w\left(w+1\right)$$

Solution Steps

Use the distributive property to multiply -w by -5w-7.

$$-5\left(-w\right)w-7\left(-w\right)-w\left(1-w\right)$$

Multiply -5 and -1 to get 5.

$$5ww-7\left(-w\right)-w\left(1-w\right)$$

Multiply w and w to get w^{2}.

$$5w^{2}-7\left(-w\right)-w\left(1-w\right)$$

Multiply -7 and -1 to get 7.

$$5w^{2}+7w-w\left(1-w\right)$$

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

$$5w^{2}+7w-\left(w-w^{2}\right)$$

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

$$5w^{2}+7w-w-\left(-w^{2}\right)$$

The opposite of -w^{2} is w^{2}.

$$5w^{2}+7w-w+w^{2}$$

Combine 7w and -w to get 6w.

$$5w^{2}+6w+w^{2}$$

Combine 5w^{2} and w^{2} to get 6w^{2}.

$$6w^{2}+6w$$

Expand

$$6w^{2}+6w$$

Solution Steps

Use the distributive property to multiply -w by -5w-7.

$$-5\left(-w\right)w-7\left(-w\right)-w\left(1-w\right)$$

Multiply -5 and -1 to get 5.

$$5ww-7\left(-w\right)-w\left(1-w\right)$$

Multiply w and w to get w^{2}.

$$5w^{2}-7\left(-w\right)-w\left(1-w\right)$$

Multiply -7 and -1 to get 7.

$$5w^{2}+7w-w\left(1-w\right)$$

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

$$5w^{2}+7w-\left(w-w^{2}\right)$$

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

$$5w^{2}+7w-w-\left(-w^{2}\right)$$

The opposite of -w^{2} is w^{2}.

$$5w^{2}+7w-w+w^{2}$$

Combine 7w and -w to get 6w.

$$5w^{2}+6w+w^{2}$$

Combine 5w^{2} and w^{2} to get 6w^{2}.

$$6w^{2}+6w$$