Solve (-1/3a+b)(3b-1/2a)

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

Evaluate

$$\frac{\left(3b-a\right)\left(6b-a\right)}{6}$$

Solution Steps

Apply the distributive property by multiplying each term of -\frac{1}{3}a+b by each term of 3b-\frac{1}{2}a.

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

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

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

Cancel out 3 and 3.

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

Multiply -\frac{1}{3} times -\frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{-\left(-1\right)}{3\times 2}.

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

Combine -ab and b\left(-\frac{1}{2}\right)a to get -\frac{3}{2}ab.

$$-\frac{3}{2}ab+\frac{1}{6}a^{2}+3b^{2}$$

Expand

$$-\frac{3ab}{2}+\frac{a^{2}}{6}+3b^{2}$$

Solution Steps

Apply the distributive property by multiplying each term of -\frac{1}{3}a+b by each term of 3b-\frac{1}{2}a.

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

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

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

Cancel out 3 and 3.

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

Multiply -\frac{1}{3} times -\frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{-\left(-1\right)}{3\times 2}.

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

Combine -ab and b\left(-\frac{1}{2}\right)a to get -\frac{3}{2}ab.

$$-\frac{3}{2}ab+\frac{1}{6}a^{2}+3b^{2}$$