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

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

Evaluate

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

Solution Steps

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

$$\frac{1}{2}a\times \frac{1}{2}a+\frac{1}{2}a\left(-3\right)+3b\times \frac{1}{2}a-9b$$

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

$$\frac{1}{2}a^{2}\times \frac{1}{2}+\frac{1}{2}a\left(-3\right)+3b\times \frac{1}{2}a-9b$$

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

$$\frac{1\times 1}{2\times 2}a^{2}+\frac{1}{2}a\left(-3\right)+3b\times \frac{1}{2}a-9b$$

Do the multiplications in the fraction \frac{1\times 1}{2\times 2}.

$$\frac{1}{4}a^{2}+\frac{1}{2}a\left(-3\right)+3b\times \frac{1}{2}a-9b$$

Multiply \frac{1}{2} and -3 to get \frac{-3}{2}.

$$\frac{1}{4}a^{2}+\frac{-3}{2}a+3b\times \frac{1}{2}a-9b$$

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

$$\frac{1}{4}a^{2}-\frac{3}{2}a+3b\times \frac{1}{2}a-9b$$

Multiply 3 and \frac{1}{2} to get \frac{3}{2}.

$$\frac{1}{4}a^{2}-\frac{3}{2}a+\frac{3}{2}ba-9b$$

Expand

$$\frac{3ab}{2}+\frac{a^{2}}{4}-\frac{3a}{2}-9b$$

Solution Steps

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

$$\frac{1}{2}a\times \frac{1}{2}a+\frac{1}{2}a\left(-3\right)+3b\times \frac{1}{2}a-9b$$

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

$$\frac{1}{2}a^{2}\times \frac{1}{2}+\frac{1}{2}a\left(-3\right)+3b\times \frac{1}{2}a-9b$$

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

$$\frac{1\times 1}{2\times 2}a^{2}+\frac{1}{2}a\left(-3\right)+3b\times \frac{1}{2}a-9b$$

Do the multiplications in the fraction \frac{1\times 1}{2\times 2}.

$$\frac{1}{4}a^{2}+\frac{1}{2}a\left(-3\right)+3b\times \frac{1}{2}a-9b$$

Multiply \frac{1}{2} and -3 to get \frac{-3}{2}.

$$\frac{1}{4}a^{2}+\frac{-3}{2}a+3b\times \frac{1}{2}a-9b$$

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

$$\frac{1}{4}a^{2}-\frac{3}{2}a+3b\times \frac{1}{2}a-9b$$

Multiply 3 and \frac{1}{2} to get \frac{3}{2}.

$$\frac{1}{4}a^{2}-\frac{3}{2}a+\frac{3}{2}ba-9b$$