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

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

Evaluate

$$8a^{2}-70ab+4a+10b$$

Solution Steps

Use the distributive property to multiply 3a by 2a+\frac{1}{3}b-1.

$$6a^{2}+3a\times \frac{1}{3}b-3a-7a\left(-\frac{2}{7}a+8b-1\right)+5b\left(-3a+2\right)$$

Cancel out 3 and 3.

$$6a^{2}+ab-3a-7a\left(-\frac{2}{7}a+8b-1\right)+5b\left(-3a+2\right)$$

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

$$6a^{2}+ab-3a-7a\left(-\frac{2}{7}a+8b-1\right)-15ba+10b$$

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

$$6a^{2}+ab-3a-7a\left(-\frac{2}{7}\right)a-56ab+7a-15ba+10b$$

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

$$6a^{2}+ab-3a-7a^{2}\left(-\frac{2}{7}\right)-56ab+7a-15ba+10b$$

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

$$6a^{2}+ab-3a+2a^{2}-56ab+7a-15ba+10b$$

Combine 6a^{2} and 2a^{2} to get 8a^{2}.

$$8a^{2}+ab-3a-56ab+7a-15ba+10b$$

Combine ab and -56ab to get -55ab.

$$8a^{2}-55ab-3a+7a-15ba+10b$$

Combine -3a and 7a to get 4a.

$$8a^{2}-55ab+4a-15ba+10b$$

Combine -55ab and -15ba to get -70ab.

$$8a^{2}-70ab+4a+10b$$

Expand

$$8a^{2}-70ab+4a+10b$$

Solution Steps

Use the distributive property to multiply 3a by 2a+\frac{1}{3}b-1.

$$6a^{2}+3a\times \frac{1}{3}b-3a-7a\left(-\frac{2}{7}a+8b-1\right)+5b\left(-3a+2\right)$$

Cancel out 3 and 3.

$$6a^{2}+ab-3a-7a\left(-\frac{2}{7}a+8b-1\right)+5b\left(-3a+2\right)$$

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

$$6a^{2}+ab-3a-7a\left(-\frac{2}{7}a+8b-1\right)-15ba+10b$$

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

$$6a^{2}+ab-3a-7a\left(-\frac{2}{7}\right)a-56ab+7a-15ba+10b$$

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

$$6a^{2}+ab-3a-7a^{2}\left(-\frac{2}{7}\right)-56ab+7a-15ba+10b$$

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

$$6a^{2}+ab-3a+2a^{2}-56ab+7a-15ba+10b$$

Combine 6a^{2} and 2a^{2} to get 8a^{2}.

$$8a^{2}+ab-3a-56ab+7a-15ba+10b$$

Combine ab and -56ab to get -55ab.

$$8a^{2}-55ab-3a+7a-15ba+10b$$

Combine -3a and 7a to get 4a.

$$8a^{2}-55ab+4a-15ba+10b$$

Combine -55ab and -15ba to get -70ab.

$$8a^{2}-70ab+4a+10b$$