Solve -[4a^{2}b+1/2a^2b-(-1/2a^2b)]+5a^2b-3ab^2=

$$- [ 4 a ^ { 2 } b + \frac { 1 } { 2 } a ^ { 2 } b - ( - \frac { 1 } { 2 } a ^ { 2 } b ) ] + 5 a ^ { 2 } b - 3 a b ^ { 2 } =$$

Evaluate

$$-3ab^{2}$$

Solution Steps

Combine 4a^{2}b and \frac{1}{2}a^{2}b to get \frac{9}{2}a^{2}b.

$$-\left(\frac{9}{2}a^{2}b-\left(-\frac{1}{2}a^{2}b\right)\right)+5a^{2}b-3ab^{2}$$

The opposite of -\frac{1}{2}a^{2}b is \frac{1}{2}a^{2}b.

$$-\left(\frac{9}{2}a^{2}b+\frac{1}{2}a^{2}b\right)+5a^{2}b-3ab^{2}$$

Combine \frac{9}{2}a^{2}b and \frac{1}{2}a^{2}b to get 5a^{2}b.

$$-5a^{2}b+5a^{2}b-3ab^{2}$$

Combine -5a^{2}b and 5a^{2}b to get 0.

$$0-3ab^{2}$$

Anything plus zero gives itself.

$$-3ab^{2}$$

Expand

$$-3ab^{2}$$

Solution Steps

Combine 4a^{2}b and \frac{1}{2}a^{2}b to get \frac{9}{2}a^{2}b.

$$-\left(\frac{9}{2}a^{2}b-\left(-\frac{1}{2}a^{2}b\right)\right)+5a^{2}b-3ab^{2}$$

The opposite of -\frac{1}{2}a^{2}b is \frac{1}{2}a^{2}b.

$$-\left(\frac{9}{2}a^{2}b+\frac{1}{2}a^{2}b\right)+5a^{2}b-3ab^{2}$$

Combine \frac{9}{2}a^{2}b and \frac{1}{2}a^{2}b to get 5a^{2}b.

$$-5a^{2}b+5a^{2}b-3ab^{2}$$

Combine -5a^{2}b and 5a^{2}b to get 0.

$$0-3ab^{2}$$

Anything plus zero gives itself.

$$-3ab^{2}$$