Solve (7/3x-5/2)(8/3x+1)

$$( \frac{ 7 }{ 3 } x- \frac{ 5 }{ 2 } )( \frac{ 8 }{ 3 } x+1)$$

Evaluate

$$\frac{56x^{2}}{9}-\frac{13x}{3}-\frac{5}{2}$$

Solution Steps

Apply the distributive property by multiplying each term of \frac{7}{3}x-\frac{5}{2} by each term of \frac{8}{3}x+1.

$$\frac{7}{3}x\times \frac{8}{3}x+\frac{7}{3}x-\frac{5}{2}\times \frac{8}{3}x-\frac{5}{2}$$

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

$$\frac{7}{3}x^{2}\times \frac{8}{3}+\frac{7}{3}x-\frac{5}{2}\times \frac{8}{3}x-\frac{5}{2}$$

Multiply \frac{7}{3} times \frac{8}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 8}{3\times 3}x^{2}+\frac{7}{3}x-\frac{5}{2}\times \frac{8}{3}x-\frac{5}{2}$$

Do the multiplications in the fraction \frac{7\times 8}{3\times 3}.

$$\frac{56}{9}x^{2}+\frac{7}{3}x-\frac{5}{2}\times \frac{8}{3}x-\frac{5}{2}$$

Multiply -\frac{5}{2} times \frac{8}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{56}{9}x^{2}+\frac{7}{3}x+\frac{-5\times 8}{2\times 3}x-\frac{5}{2}$$

Do the multiplications in the fraction \frac{-5\times 8}{2\times 3}.

$$\frac{56}{9}x^{2}+\frac{7}{3}x+\frac{-40}{6}x-\frac{5}{2}$$

Reduce the fraction \frac{-40}{6} to lowest terms by extracting and canceling out 2.

$$\frac{56}{9}x^{2}+\frac{7}{3}x-\frac{20}{3}x-\frac{5}{2}$$

Combine \frac{7}{3}x and -\frac{20}{3}x to get -\frac{13}{3}x.

$$\frac{56}{9}x^{2}-\frac{13}{3}x-\frac{5}{2}$$

Expand

$$\frac{56x^{2}}{9}-\frac{13x}{3}-\frac{5}{2}$$

Solution Steps

Apply the distributive property by multiplying each term of \frac{7}{3}x-\frac{5}{2} by each term of \frac{8}{3}x+1.

$$\frac{7}{3}x\times \frac{8}{3}x+\frac{7}{3}x-\frac{5}{2}\times \frac{8}{3}x-\frac{5}{2}$$

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

$$\frac{7}{3}x^{2}\times \frac{8}{3}+\frac{7}{3}x-\frac{5}{2}\times \frac{8}{3}x-\frac{5}{2}$$

Multiply \frac{7}{3} times \frac{8}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 8}{3\times 3}x^{2}+\frac{7}{3}x-\frac{5}{2}\times \frac{8}{3}x-\frac{5}{2}$$

Do the multiplications in the fraction \frac{7\times 8}{3\times 3}.

$$\frac{56}{9}x^{2}+\frac{7}{3}x-\frac{5}{2}\times \frac{8}{3}x-\frac{5}{2}$$

Multiply -\frac{5}{2} times \frac{8}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{56}{9}x^{2}+\frac{7}{3}x+\frac{-5\times 8}{2\times 3}x-\frac{5}{2}$$

Do the multiplications in the fraction \frac{-5\times 8}{2\times 3}.

$$\frac{56}{9}x^{2}+\frac{7}{3}x+\frac{-40}{6}x-\frac{5}{2}$$

Reduce the fraction \frac{-40}{6} to lowest terms by extracting and canceling out 2.

$$\frac{56}{9}x^{2}+\frac{7}{3}x-\frac{20}{3}x-\frac{5}{2}$$

Combine \frac{7}{3}x and -\frac{20}{3}x to get -\frac{13}{3}x.

$$\frac{56}{9}x^{2}-\frac{13}{3}x-\frac{5}{2}$$