Solve -lambda[-lambda(191-lambda)-3gamma2^2]

$$- \lambda [ - \lambda ( 191 - \lambda ) - 3 \gamma 2 ^ { 2 } ]$$

Evaluate

$$-\lambda \left(\lambda ^{2}-12\gamma -191\lambda \right)$$

Solution Steps

Use the distributive property to multiply -\lambda by 191-\lambda .

$$\left(-\lambda \right)\left(191\left(-\lambda \right)-\left(-\lambda \right)\lambda -3\gamma \times 2^{2}\right)$$

Multiply -1 and -1 to get 1.

$$\left(-\lambda \right)\left(191\left(-\lambda \right)+\lambda \lambda -3\gamma \times 2^{2}\right)$$

Multiply \lambda and \lambda to get \lambda ^{2}.

$$\left(-\lambda \right)\left(191\left(-\lambda \right)+\lambda ^{2}-3\gamma \times 2^{2}\right)$$

Calculate 2 to the power of 2 and get 4.

$$\left(-\lambda \right)\left(191\left(-\lambda \right)+\lambda ^{2}-3\gamma \times 4\right)$$

Multiply 3 and 4 to get 12.

$$\left(-\lambda \right)\left(191\left(-\lambda \right)+\lambda ^{2}-12\gamma \right)$$

Use the distributive property to multiply -\lambda by 191\left(-\lambda \right)+\lambda ^{2}-12\gamma .

$$191\left(-\lambda \right)^{2}+\left(-\lambda \right)\lambda ^{2}-12\left(-\lambda \right)\gamma$$

Calculate -\lambda to the power of 2 and get \lambda ^{2}.

$$191\lambda ^{2}+\left(-\lambda \right)\lambda ^{2}-12\left(-\lambda \right)\gamma$$

Multiply -12 and -1 to get 12.

$$191\lambda ^{2}+\left(-\lambda \right)\lambda ^{2}+12\lambda \gamma$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$191\lambda ^{2}-\lambda ^{3}+12\lambda \gamma$$

Expand

$$12\gamma \lambda -\lambda ^{3}+191\lambda ^{2}$$

Solution Steps

Use the distributive property to multiply -\lambda by 191-\lambda .

$$\left(-\lambda \right)\left(191\left(-\lambda \right)-\left(-\lambda \right)\lambda -3\gamma \times 2^{2}\right)$$

Multiply -1 and -1 to get 1.

$$\left(-\lambda \right)\left(191\left(-\lambda \right)+\lambda \lambda -3\gamma \times 2^{2}\right)$$

Multiply \lambda and \lambda to get \lambda ^{2}.

$$\left(-\lambda \right)\left(191\left(-\lambda \right)+\lambda ^{2}-3\gamma \times 2^{2}\right)$$

Calculate 2 to the power of 2 and get 4.

$$\left(-\lambda \right)\left(191\left(-\lambda \right)+\lambda ^{2}-3\gamma \times 4\right)$$

Multiply 3 and 4 to get 12.

$$\left(-\lambda \right)\left(191\left(-\lambda \right)+\lambda ^{2}-12\gamma \right)$$

Use the distributive property to multiply -\lambda by 191\left(-\lambda \right)+\lambda ^{2}-12\gamma .

$$191\left(-\lambda \right)^{2}+\left(-\lambda \right)\lambda ^{2}-12\left(-\lambda \right)\gamma$$

Calculate -\lambda to the power of 2 and get \lambda ^{2}.

$$191\lambda ^{2}+\left(-\lambda \right)\lambda ^{2}-12\left(-\lambda \right)\gamma$$

Multiply -12 and -1 to get 12.

$$191\lambda ^{2}+\left(-\lambda \right)\lambda ^{2}+12\lambda \gamma$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$191\lambda ^{2}-\lambda ^{3}+12\lambda \gamma$$