Solve pi(2/3x+6/5)(2/3x-6/5)

$$\pi ( \frac { 2 } { 3 } x + \frac { 6 } { 5 } ) ( \frac { 2 } { 3 } x - \frac { 6 } { 5 } )$$

Evaluate

$$\frac{4\pi x^{2}}{9}-\frac{36\pi }{25}$$

Solution Steps

Use the distributive property to multiply \pi by \frac{2}{3}x+\frac{6}{5}.

$$\left(\pi \times \frac{2}{3}x+\pi \times \frac{6}{5}\right)\left(\frac{2}{3}x-\frac{6}{5}\right)$$

Apply the distributive property by multiplying each term of \pi \times \frac{2}{3}x+\pi \times \frac{6}{5} by each term of \frac{2}{3}x-\frac{6}{5}.

$$\pi \times \frac{2}{3}x\times \frac{2}{3}x+\pi \times \frac{2}{3}x\left(-\frac{6}{5}\right)+\pi \times \frac{6}{5}\times \frac{2}{3}x+\pi \times \frac{6}{5}\left(-\frac{6}{5}\right)$$

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

$$\pi \times \frac{2}{3}x^{2}\times \frac{2}{3}+\pi \times \frac{2}{3}x\left(-\frac{6}{5}\right)+\pi \times \frac{6}{5}\times \frac{2}{3}x+\pi \times \frac{6}{5}\left(-\frac{6}{5}\right)$$

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

$$\pi \times \frac{2\times 2}{3\times 3}x^{2}+\pi \times \frac{2}{3}x\left(-\frac{6}{5}\right)+\pi \times \frac{6}{5}\times \frac{2}{3}x+\pi \times \frac{6}{5}\left(-\frac{6}{5}\right)$$

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

$$\pi \times \frac{4}{9}x^{2}+\pi \times \frac{2}{3}x\left(-\frac{6}{5}\right)+\pi \times \frac{6}{5}\times \frac{2}{3}x+\pi \times \frac{6}{5}\left(-\frac{6}{5}\right)$$

Multiply \frac{2}{3} times -\frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$\pi \times \frac{4}{9}x^{2}+\pi \times \frac{2\left(-6\right)}{3\times 5}x+\pi \times \frac{6}{5}\times \frac{2}{3}x+\pi \times \frac{6}{5}\left(-\frac{6}{5}\right)$$

Do the multiplications in the fraction \frac{2\left(-6\right)}{3\times 5}.

$$\pi \times \frac{4}{9}x^{2}+\pi \times \frac{-12}{15}x+\pi \times \frac{6}{5}\times \frac{2}{3}x+\pi \times \frac{6}{5}\left(-\frac{6}{5}\right)$$

Reduce the fraction \frac{-12}{15} to lowest terms by extracting and canceling out 3.

$$\pi \times \frac{4}{9}x^{2}+\pi \left(-\frac{4}{5}\right)x+\pi \times \frac{6}{5}\times \frac{2}{3}x+\pi \times \frac{6}{5}\left(-\frac{6}{5}\right)$$

Multiply \frac{6}{5} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\pi \times \frac{4}{9}x^{2}+\pi \left(-\frac{4}{5}\right)x+\pi \times \frac{6\times 2}{5\times 3}x+\pi \times \frac{6}{5}\left(-\frac{6}{5}\right)$$

Do the multiplications in the fraction \frac{6\times 2}{5\times 3}.

$$\pi \times \frac{4}{9}x^{2}+\pi \left(-\frac{4}{5}\right)x+\pi \times \frac{12}{15}x+\pi \times \frac{6}{5}\left(-\frac{6}{5}\right)$$

Reduce the fraction \frac{12}{15} to lowest terms by extracting and canceling out 3.

$$\pi \times \frac{4}{9}x^{2}+\pi \left(-\frac{4}{5}\right)x+\pi \times \frac{4}{5}x+\pi \times \frac{6}{5}\left(-\frac{6}{5}\right)$$

Combine \pi \left(-\frac{4}{5}\right)x and \pi \times \frac{4}{5}x to get 0.

$$\pi \times \frac{4}{9}x^{2}+\pi \times \frac{6}{5}\left(-\frac{6}{5}\right)$$

Multiply \frac{6}{5} times -\frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$\pi \times \frac{4}{9}x^{2}+\pi \times \frac{6\left(-6\right)}{5\times 5}$$

Do the multiplications in the fraction \frac{6\left(-6\right)}{5\times 5}.

$$\pi \times \frac{4}{9}x^{2}+\pi \times \frac{-36}{25}$$

Fraction \frac{-36}{25} can be rewritten as -\frac{36}{25} by extracting the negative sign.

$$\pi \times \frac{4}{9}x^{2}+\pi \left(-\frac{36}{25}\right)$$

Expand

$$\frac{4\pi x^{2}}{9}-\frac{36\pi }{25}$$

Solution Steps

Use the distributive property to multiply \pi by \frac{2}{3}x+\frac{6}{5}.

$$\left(\pi \times \frac{2}{3}x+\pi \times \frac{6}{5}\right)\left(\frac{2}{3}x-\frac{6}{5}\right)$$

Apply the distributive property by multiplying each term of \pi \times \frac{2}{3}x+\pi \times \frac{6}{5} by each term of \frac{2}{3}x-\frac{6}{5}.

$$\pi \times \frac{2}{3}x\times \frac{2}{3}x+\pi \times \frac{2}{3}x\left(-\frac{6}{5}\right)+\pi \times \frac{6}{5}\times \frac{2}{3}x+\pi \times \frac{6}{5}\left(-\frac{6}{5}\right)$$

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

$$\pi \times \frac{2}{3}x^{2}\times \frac{2}{3}+\pi \times \frac{2}{3}x\left(-\frac{6}{5}\right)+\pi \times \frac{6}{5}\times \frac{2}{3}x+\pi \times \frac{6}{5}\left(-\frac{6}{5}\right)$$

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

$$\pi \times \frac{2\times 2}{3\times 3}x^{2}+\pi \times \frac{2}{3}x\left(-\frac{6}{5}\right)+\pi \times \frac{6}{5}\times \frac{2}{3}x+\pi \times \frac{6}{5}\left(-\frac{6}{5}\right)$$

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

$$\pi \times \frac{4}{9}x^{2}+\pi \times \frac{2}{3}x\left(-\frac{6}{5}\right)+\pi \times \frac{6}{5}\times \frac{2}{3}x+\pi \times \frac{6}{5}\left(-\frac{6}{5}\right)$$

Multiply \frac{2}{3} times -\frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$\pi \times \frac{4}{9}x^{2}+\pi \times \frac{2\left(-6\right)}{3\times 5}x+\pi \times \frac{6}{5}\times \frac{2}{3}x+\pi \times \frac{6}{5}\left(-\frac{6}{5}\right)$$

Do the multiplications in the fraction \frac{2\left(-6\right)}{3\times 5}.

$$\pi \times \frac{4}{9}x^{2}+\pi \times \frac{-12}{15}x+\pi \times \frac{6}{5}\times \frac{2}{3}x+\pi \times \frac{6}{5}\left(-\frac{6}{5}\right)$$

Reduce the fraction \frac{-12}{15} to lowest terms by extracting and canceling out 3.

$$\pi \times \frac{4}{9}x^{2}+\pi \left(-\frac{4}{5}\right)x+\pi \times \frac{6}{5}\times \frac{2}{3}x+\pi \times \frac{6}{5}\left(-\frac{6}{5}\right)$$

Multiply \frac{6}{5} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\pi \times \frac{4}{9}x^{2}+\pi \left(-\frac{4}{5}\right)x+\pi \times \frac{6\times 2}{5\times 3}x+\pi \times \frac{6}{5}\left(-\frac{6}{5}\right)$$

Do the multiplications in the fraction \frac{6\times 2}{5\times 3}.

$$\pi \times \frac{4}{9}x^{2}+\pi \left(-\frac{4}{5}\right)x+\pi \times \frac{12}{15}x+\pi \times \frac{6}{5}\left(-\frac{6}{5}\right)$$

Reduce the fraction \frac{12}{15} to lowest terms by extracting and canceling out 3.

$$\pi \times \frac{4}{9}x^{2}+\pi \left(-\frac{4}{5}\right)x+\pi \times \frac{4}{5}x+\pi \times \frac{6}{5}\left(-\frac{6}{5}\right)$$

Combine \pi \left(-\frac{4}{5}\right)x and \pi \times \frac{4}{5}x to get 0.

$$\pi \times \frac{4}{9}x^{2}+\pi \times \frac{6}{5}\left(-\frac{6}{5}\right)$$

Multiply \frac{6}{5} times -\frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$\pi \times \frac{4}{9}x^{2}+\pi \times \frac{6\left(-6\right)}{5\times 5}$$

Do the multiplications in the fraction \frac{6\left(-6\right)}{5\times 5}.

$$\pi \times \frac{4}{9}x^{2}+\pi \times \frac{-36}{25}$$

Fraction \frac{-36}{25} can be rewritten as -\frac{36}{25} by extracting the negative sign.

$$\pi \times \frac{4}{9}x^{2}+\pi \left(-\frac{36}{25}\right)$$