Solve (a+3b)+1/2b^2-(a-2b)-3a^2*(a+7/3)

$$( a + 3 b ) + \frac { 1 } { 2 } b ^ { 2 } - ( a - 2 b ) - 3 a ^ { 2 } \cdot ( a + \frac { 7 } { 3 } )$$

Evaluate

$$-3a^{3}+\frac{b^{2}}{2}-7a^{2}+5b$$

Solution Steps

To find the opposite of a-2b, find the opposite of each term.

$$a+3b+\frac{1}{2}b^{2}-a+2b-3a^{2}\left(a+\frac{7}{3}\right)$$

Combine a and -a to get 0.

$$3b+\frac{1}{2}b^{2}+2b-3a^{2}\left(a+\frac{7}{3}\right)$$

Combine 3b and 2b to get 5b.

$$5b+\frac{1}{2}b^{2}-3a^{2}\left(a+\frac{7}{3}\right)$$

Use the distributive property to multiply -3a^{2} by a+\frac{7}{3}.

$$5b+\frac{1}{2}b^{2}-3a^{3}-7a^{2}$$

Expand

$$-3a^{3}+\frac{b^{2}}{2}-7a^{2}+5b$$

Solution Steps

To find the opposite of a-2b, find the opposite of each term.

$$a+3b+\frac{1}{2}b^{2}-a+2b-3a^{2}\left(a+\frac{7}{3}\right)$$

Combine a and -a to get 0.

$$3b+\frac{1}{2}b^{2}+2b-3a^{2}\left(a+\frac{7}{3}\right)$$

Combine 3b and 2b to get 5b.

$$5b+\frac{1}{2}b^{2}-3a^{2}\left(a+\frac{7}{3}\right)$$

Use the distributive property to multiply -3a^{2} by a+\frac{7}{3}.

$$5b+\frac{1}{2}b^{2}-3a^{3}-7a^{2}$$