Solve 2c(c+d)+5c^2-d(c-d)

$$2 c ( c + d ) + 5 c ^ { 2 } - d ( c - d )$$

Evaluate

$$7c^{2}+cd+d^{2}$$

Solution Steps

Use the distributive property to multiply 2c by c+d.

$$2c^{2}+2cd+5c^{2}-d\left(c-d\right)$$

Combine 2c^{2} and 5c^{2} to get 7c^{2}.

$$7c^{2}+2cd-d\left(c-d\right)$$

Use the distributive property to multiply d by c-d.

$$7c^{2}+2cd-\left(dc-d^{2}\right)$$

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

$$7c^{2}+2cd-dc+d^{2}$$

Combine 2cd and -dc to get cd.

$$7c^{2}+cd+d^{2}$$

Expand

$$7c^{2}+cd+d^{2}$$

Solution Steps

Use the distributive property to multiply 2c by c+d.

$$2c^{2}+2cd+5c^{2}-d\left(c-d\right)$$

Combine 2c^{2} and 5c^{2} to get 7c^{2}.

$$7c^{2}+2cd-d\left(c-d\right)$$

Use the distributive property to multiply d by c-d.

$$7c^{2}+2cd-\left(dc-d^{2}\right)$$

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

$$7c^{2}+2cd-dc+d^{2}$$

Combine 2cd and -dc to get cd.

$$7c^{2}+cd+d^{2}$$