Solve 4b-3a(4/a+6b-2b/a)

$$4 b - 3 a ( \frac { 4 } { a } + 6 b - \frac { 2 b } { a } )$$

Evaluate

$$-18ab+10b-12$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 6b times \frac{a}{a}.

$$4b-3a\left(\frac{4}{a}+\frac{6ba}{a}-\frac{2b}{a}\right)$$

Since \frac{4}{a} and \frac{6ba}{a} have the same denominator, add them by adding their numerators.

$$4b-3a\left(\frac{4+6ba}{a}-\frac{2b}{a}\right)$$

Since \frac{4+6ba}{a} and \frac{2b}{a} have the same denominator, subtract them by subtracting their numerators.

$$4b-3a\times \frac{4+6ba-2b}{a}$$

Express 3\times \frac{4+6ba-2b}{a} as a single fraction.

$$4b-\frac{3\left(4+6ba-2b\right)}{a}a$$

Use the distributive property to multiply 3 by 4+6ba-2b.

$$4b-\frac{12+18ba-6b}{a}a$$

Cancel out a and a.

$$4b-\left(12+18ba-6b\right)$$

To find the opposite of 12+18ba-6b, find the opposite of each term.

$$4b-12-18ba-\left(-6b\right)$$

The opposite of -6b is 6b.

$$4b-12-18ba+6b$$

Combine 4b and 6b to get 10b.

$$10b-12-18ba$$

Expand

$$-18ab+10b-12$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 6b times \frac{a}{a}.

$$4b-3a\left(\frac{4}{a}+\frac{6ba}{a}-\frac{2b}{a}\right)$$

Since \frac{4}{a} and \frac{6ba}{a} have the same denominator, add them by adding their numerators.

$$4b-3a\left(\frac{4+6ba}{a}-\frac{2b}{a}\right)$$

Since \frac{4+6ba}{a} and \frac{2b}{a} have the same denominator, subtract them by subtracting their numerators.

$$4b-3a\times \frac{4+6ba-2b}{a}$$

Express 3\times \frac{4+6ba-2b}{a} as a single fraction.

$$4b-\frac{3\left(4+6ba-2b\right)}{a}a$$

Use the distributive property to multiply 3 by 4+6ba-2b.

$$4b-\frac{12+18ba-6b}{a}a$$

Cancel out a and a.

$$4b-\left(12+18ba-6b\right)$$

To find the opposite of 12+18ba-6b, find the opposite of each term.

$$4b-12-18ba-\left(-6b\right)$$

The opposite of -6b is 6b.

$$4b-12-18ba+6b$$

Combine 4b and 6b to get 10b.

$$10b-12-18ba$$