Solve (c-1)(c-2)+(c-3)(c-4)

$$( c - 1 ) ( c - 2 ) + ( c - 3 ) ( c - 4 )$$

Evaluate

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

Solution Steps

Apply the distributive property by multiplying each term of c-1 by each term of c-2.

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

Combine -2c and -c to get -3c.

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

Apply the distributive property by multiplying each term of c-3 by each term of c-4.

$$c^{2}-3c+2+c^{2}-4c-3c+12$$

Combine -4c and -3c to get -7c.

$$c^{2}-3c+2+c^{2}-7c+12$$

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

$$2c^{2}-3c+2-7c+12$$

Combine -3c and -7c to get -10c.

$$2c^{2}-10c+2+12$$

Add 2 and 12 to get 14.

$$2c^{2}-10c+14$$

Expand

$$2c^{2}-10c+14$$

Solution Steps

Apply the distributive property by multiplying each term of c-1 by each term of c-2.

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

Combine -2c and -c to get -3c.

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

Apply the distributive property by multiplying each term of c-3 by each term of c-4.

$$c^{2}-3c+2+c^{2}-4c-3c+12$$

Combine -4c and -3c to get -7c.

$$c^{2}-3c+2+c^{2}-7c+12$$

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

$$2c^{2}-3c+2-7c+12$$

Combine -3c and -7c to get -10c.

$$2c^{2}-10c+2+12$$

Add 2 and 12 to get 14.

$$2c^{2}-10c+14$$