Solve (3/2d+5)(3/2partial-5)

$$( \frac { 3 } { 2 } d + 5 ) ( \frac { 3 } { 2 } \partial - 5 )$$

Evaluate

$$\frac{\left(3∂-10\right)\left(3d+10\right)}{4}$$

Solution Steps

Apply the distributive property by multiplying each term of \frac{3}{2}d+5 by each term of \frac{3}{2}∂-5.

$$\frac{3}{2}d\times \frac{3}{2}∂+\frac{3}{2}d\left(-5\right)+5\times \frac{3}{2}∂-25$$

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

$$\frac{3\times 3}{2\times 2}d∂+\frac{3}{2}d\left(-5\right)+5\times \frac{3}{2}∂-25$$

Do the multiplications in the fraction \frac{3\times 3}{2\times 2}.

$$\frac{9}{4}d∂+\frac{3}{2}d\left(-5\right)+5\times \frac{3}{2}∂-25$$

Express \frac{3}{2}\left(-5\right) as a single fraction.

$$\frac{9}{4}d∂+\frac{3\left(-5\right)}{2}d+5\times \frac{3}{2}∂-25$$

Multiply 3 and -5 to get -15.

$$\frac{9}{4}d∂+\frac{-15}{2}d+5\times \frac{3}{2}∂-25$$

Fraction \frac{-15}{2} can be rewritten as -\frac{15}{2} by extracting the negative sign.

$$\frac{9}{4}d∂-\frac{15}{2}d+5\times \frac{3}{2}∂-25$$

Express 5\times \frac{3}{2} as a single fraction.

$$\frac{9}{4}d∂-\frac{15}{2}d+\frac{5\times 3}{2}∂-25$$

Multiply 5 and 3 to get 15.

$$\frac{9}{4}d∂-\frac{15}{2}d+\frac{15}{2}∂-25$$

Expand

$$\frac{9d∂}{4}+\frac{15∂}{2}-\frac{15d}{2}-25$$

Solution Steps

Apply the distributive property by multiplying each term of \frac{3}{2}d+5 by each term of \frac{3}{2}∂-5.

$$\frac{3}{2}d\times \frac{3}{2}∂+\frac{3}{2}d\left(-5\right)+5\times \frac{3}{2}∂-25$$

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

$$\frac{3\times 3}{2\times 2}d∂+\frac{3}{2}d\left(-5\right)+5\times \frac{3}{2}∂-25$$

Do the multiplications in the fraction \frac{3\times 3}{2\times 2}.

$$\frac{9}{4}d∂+\frac{3}{2}d\left(-5\right)+5\times \frac{3}{2}∂-25$$

Express \frac{3}{2}\left(-5\right) as a single fraction.

$$\frac{9}{4}d∂+\frac{3\left(-5\right)}{2}d+5\times \frac{3}{2}∂-25$$

Multiply 3 and -5 to get -15.

$$\frac{9}{4}d∂+\frac{-15}{2}d+5\times \frac{3}{2}∂-25$$

Fraction \frac{-15}{2} can be rewritten as -\frac{15}{2} by extracting the negative sign.

$$\frac{9}{4}d∂-\frac{15}{2}d+5\times \frac{3}{2}∂-25$$

Express 5\times \frac{3}{2} as a single fraction.

$$\frac{9}{4}d∂-\frac{15}{2}d+\frac{5\times 3}{2}∂-25$$

Multiply 5 and 3 to get 15.

$$\frac{9}{4}d∂-\frac{15}{2}d+\frac{15}{2}∂-25$$