Solve (2a+1/3b-1)-7a(-2/7a+8b-1)+5b(-3a+2)

$$( 2 a + \frac { 1 } { 3 } b - 1 ) - 7 a ( - \frac { 2 } { 7 } a + 8 b - 1 ) + 5 b ( - 3 a + 2 )$$

Evaluate

$$-71ab+2a^{2}+\frac{31b}{3}+9a-1$$

Solution Steps

Use the distributive property to multiply 5b by -3a+2.

$$2a+\frac{1}{3}b-1-7a\left(-\frac{2}{7}a+8b-1\right)-15ba+10b$$

Use the distributive property to multiply -7a by -\frac{2}{7}a+8b-1.

$$2a+\frac{1}{3}b-1-7a\left(-\frac{2}{7}\right)a-56ab+7a-15ba+10b$$

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

$$2a+\frac{1}{3}b-1-7a^{2}\left(-\frac{2}{7}\right)-56ab+7a-15ba+10b$$

Multiply -7 times -\frac{2}{7}.

$$2a+\frac{1}{3}b-1+2a^{2}-56ab+7a-15ba+10b$$

Combine 2a and 7a to get 9a.

$$9a+\frac{1}{3}b-1+2a^{2}-56ab-15ba+10b$$

Combine -56ab and -15ba to get -71ab.

$$9a+\frac{1}{3}b-1+2a^{2}-71ab+10b$$

Combine \frac{1}{3}b and 10b to get \frac{31}{3}b.

$$9a+\frac{31}{3}b-1+2a^{2}-71ab$$

Expand

$$-71ab+2a^{2}+\frac{31b}{3}+9a-1$$

Solution Steps

Use the distributive property to multiply 5b by -3a+2.

$$2a+\frac{1}{3}b-1-7a\left(-\frac{2}{7}a+8b-1\right)-15ba+10b$$

Use the distributive property to multiply -7a by -\frac{2}{7}a+8b-1.

$$2a+\frac{1}{3}b-1-7a\left(-\frac{2}{7}\right)a-56ab+7a-15ba+10b$$

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

$$2a+\frac{1}{3}b-1-7a^{2}\left(-\frac{2}{7}\right)-56ab+7a-15ba+10b$$

Multiply -7 times -\frac{2}{7}.

$$2a+\frac{1}{3}b-1+2a^{2}-56ab+7a-15ba+10b$$

Combine 2a and 7a to get 9a.

$$9a+\frac{1}{3}b-1+2a^{2}-56ab-15ba+10b$$

Combine -56ab and -15ba to get -71ab.

$$9a+\frac{1}{3}b-1+2a^{2}-71ab+10b$$

Combine \frac{1}{3}b and 10b to get \frac{31}{3}b.

$$9a+\frac{31}{3}b-1+2a^{2}-71ab$$