Solve 2ab-3(b(4a-1)-b(6-10a))+7b

$$2 a b - 3 ( b ( 4 a - 1 ) - b ( 6 - 10 a ) ) + 7 b$$

Evaluate

$$28b-40ab$$

Solution Steps

Use the distributive property to multiply b by 4a-1.

$$2ab-3\left(4ba-b-b\left(6-10a\right)\right)+7b$$

Use the distributive property to multiply b by 6-10a.

$$2ab-3\left(4ba-b-\left(6b-10ba\right)\right)+7b$$

To find the opposite of 6b-10ba, find the opposite of each term.

$$2ab-3\left(4ba-b-6b-\left(-10ba\right)\right)+7b$$

The opposite of -10ba is 10ba.

$$2ab-3\left(4ba-b-6b+10ba\right)+7b$$

Combine -b and -6b to get -7b.

$$2ab-3\left(4ba-7b+10ba\right)+7b$$

Combine 4ba and 10ba to get 14ba.

$$2ab-3\left(14ba-7b\right)+7b$$

Use the distributive property to multiply -3 by 14ba-7b.

$$2ab-42ba+21b+7b$$

Combine 2ab and -42ba to get -40ab.

$$-40ab+21b+7b$$

Combine 21b and 7b to get 28b.

$$-40ab+28b$$

Expand

$$28b-40ab$$

Solution Steps

Use the distributive property to multiply b by 4a-1.

$$2ab-3\left(4ba-b-b\left(6-10a\right)\right)+7b$$

Use the distributive property to multiply b by 6-10a.

$$2ab-3\left(4ba-b-\left(6b-10ba\right)\right)+7b$$

To find the opposite of 6b-10ba, find the opposite of each term.

$$2ab-3\left(4ba-b-6b-\left(-10ba\right)\right)+7b$$

The opposite of -10ba is 10ba.

$$2ab-3\left(4ba-b-6b+10ba\right)+7b$$

Combine -b and -6b to get -7b.

$$2ab-3\left(4ba-7b+10ba\right)+7b$$

Combine 4ba and 10ba to get 14ba.

$$2ab-3\left(14ba-7b\right)+7b$$

Use the distributive property to multiply -3 by 14ba-7b.

$$2ab-42ba+21b+7b$$

Combine 2ab and -42ba to get -40ab.

$$-40ab+21b+7b$$

Combine 21b and 7b to get 28b.

$$-40ab+28b$$