Solve (c+2d)^2-(c+2d)(3c-7d)=

$$( c + 2 d ) ^ { 2 } - ( c + 2 d ) ( 3 c - 7 d ) =$$

Evaluate

$$\left(9d-2c\right)\left(c+2d\right)$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(c+2d\right)^{2}.

$$c^{2}+4cd+4d^{2}-\left(c+2d\right)\left(3c-7d\right)$$

Use the distributive property to multiply c+2d by 3c-7d and combine like terms.

$$c^{2}+4cd+4d^{2}-\left(3c^{2}-cd-14d^{2}\right)$$

To find the opposite of 3c^{2}-cd-14d^{2}, find the opposite of each term.

$$c^{2}+4cd+4d^{2}-3c^{2}+cd+14d^{2}$$

Combine c^{2} and -3c^{2} to get -2c^{2}.

$$-2c^{2}+4cd+4d^{2}+cd+14d^{2}$$

Combine 4cd and cd to get 5cd.

$$-2c^{2}+5cd+4d^{2}+14d^{2}$$

Combine 4d^{2} and 14d^{2} to get 18d^{2}.

$$-2c^{2}+5cd+18d^{2}$$

Expand

$$18d^{2}+5cd-2c^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(c+2d\right)^{2}.

$$c^{2}+4cd+4d^{2}-\left(c+2d\right)\left(3c-7d\right)$$

Use the distributive property to multiply c+2d by 3c-7d and combine like terms.

$$c^{2}+4cd+4d^{2}-\left(3c^{2}-cd-14d^{2}\right)$$

To find the opposite of 3c^{2}-cd-14d^{2}, find the opposite of each term.

$$c^{2}+4cd+4d^{2}-3c^{2}+cd+14d^{2}$$

Combine c^{2} and -3c^{2} to get -2c^{2}.

$$-2c^{2}+4cd+4d^{2}+cd+14d^{2}$$

Combine 4cd and cd to get 5cd.

$$-2c^{2}+5cd+4d^{2}+14d^{2}$$

Combine 4d^{2} and 14d^{2} to get 18d^{2}.

$$-2c^{2}+5cd+18d^{2}$$