Solve 7*(k-2)+2*(lambda-1)+(k-2)*(-7+lambda)-klambda

$$7 \cdot ( k - 2 ) + 2 \cdot ( \lambda - 1 ) + ( k - 2 ) \cdot ( - 7 + \lambda ) - k \lambda$$

Evaluate

$$-2$$

Solution Steps

Use the distributive property to multiply 7 by k-2.

$$7k-14+2\left(\lambda -1\right)+\left(k-2\right)\left(-7+\lambda \right)-k\lambda$$

Use the distributive property to multiply 2 by \lambda -1.

$$7k-14+2\lambda -2+\left(k-2\right)\left(-7+\lambda \right)-k\lambda$$

Subtract 2 from -14 to get -16.

$$7k-16+2\lambda +\left(k-2\right)\left(-7+\lambda \right)-k\lambda$$

Apply the distributive property by multiplying each term of k-2 by each term of -7+\lambda .

$$7k-16+2\lambda -7k+k\lambda +14-2\lambda -k\lambda$$

Combine 7k and -7k to get 0.

$$-16+2\lambda +k\lambda +14-2\lambda -k\lambda$$

Add -16 and 14 to get -2.

$$-2+2\lambda +k\lambda -2\lambda -k\lambda$$

Combine 2\lambda and -2\lambda to get 0.

$$-2+k\lambda -k\lambda$$

Combine k\lambda and -k\lambda to get 0.

$$-2$$

Factor

$$-2$$