Solve 1/2ab(-4a)+2b*(-1/2a^2)+3a^2b-(3a^2b-5a^2b)

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

Evaluate

$$2ba^{2}$$

Solution Steps

Multiply a and a to get a^{2}.

$$\frac{1}{2}a^{2}b\left(-4\right)+2b\left(-\frac{1}{2}\right)a^{2}+3a^{2}b-\left(3a^{2}b-5a^{2}b\right)$$

Multiply \frac{1}{2} and -4 to get -2.

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

Multiply 2 and -\frac{1}{2} to get -1.

$$-2a^{2}b-ba^{2}+3a^{2}b-\left(3a^{2}b-5a^{2}b\right)$$

Combine -2a^{2}b and -ba^{2} to get -3a^{2}b.

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

Combine -3a^{2}b and 3a^{2}b to get 0.

$$0-\left(3a^{2}b-5a^{2}b\right)$$

Combine 3a^{2}b and -5a^{2}b to get -2a^{2}b.

$$0-\left(-2a^{2}b\right)$$

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

$$0+2a^{2}b$$

Anything plus zero gives itself.

$$2a^{2}b$$

Expand

$$2ba^{2}$$

Solution Steps

Multiply a and a to get a^{2}.

$$\frac{1}{2}a^{2}b\left(-4\right)+2b\left(-\frac{1}{2}\right)a^{2}+3a^{2}b-\left(3a^{2}b-5a^{2}b\right)$$

Multiply \frac{1}{2} and -4 to get -2.

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

Multiply 2 and -\frac{1}{2} to get -1.

$$-2a^{2}b-ba^{2}+3a^{2}b-\left(3a^{2}b-5a^{2}b\right)$$

Combine -2a^{2}b and -ba^{2} to get -3a^{2}b.

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

Combine -3a^{2}b and 3a^{2}b to get 0.

$$0-\left(3a^{2}b-5a^{2}b\right)$$

Combine 3a^{2}b and -5a^{2}b to get -2a^{2}b.

$$0-\left(-2a^{2}b\right)$$

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

$$0+2a^{2}b$$

Anything plus zero gives itself.

$$2a^{2}b$$