Solve 125left(4x-1/8right)+{left(3/4right)}^2

$$125 \left( 4x- \frac{ 1 }{ 8 } \right) + { \left( \frac{ 3 }{ 4 } \right) }^{ 2 }$$

Evaluate

$$500x-\frac{241}{16}$$

Solution Steps

Use the distributive property to multiply 125 by 4x-\frac{1}{8}.

$$500x+125\left(-\frac{1}{8}\right)+\left(\frac{3}{4}\right)^{2}$$

Express 125\left(-\frac{1}{8}\right) as a single fraction.

$$500x+\frac{125\left(-1\right)}{8}+\left(\frac{3}{4}\right)^{2}$$

Multiply 125 and -1 to get -125.

$$500x+\frac{-125}{8}+\left(\frac{3}{4}\right)^{2}$$

Fraction \frac{-125}{8} can be rewritten as -\frac{125}{8} by extracting the negative sign.

$$500x-\frac{125}{8}+\left(\frac{3}{4}\right)^{2}$$

Calculate \frac{3}{4} to the power of 2 and get \frac{9}{16}.

$$500x-\frac{125}{8}+\frac{9}{16}$$

Least common multiple of 8 and 16 is 16. Convert -\frac{125}{8} and \frac{9}{16} to fractions with denominator 16.

$$500x-\frac{250}{16}+\frac{9}{16}$$

Since -\frac{250}{16} and \frac{9}{16} have the same denominator, add them by adding their numerators.

$$500x+\frac{-250+9}{16}$$

Add -250 and 9 to get -241.

$$500x-\frac{241}{16}$$

Expand

$$500x-\frac{241}{16}$$

Solution Steps

Use the distributive property to multiply 125 by 4x-\frac{1}{8}.

$$500x+125\left(-\frac{1}{8}\right)+\left(\frac{3}{4}\right)^{2}$$

Express 125\left(-\frac{1}{8}\right) as a single fraction.

$$500x+\frac{125\left(-1\right)}{8}+\left(\frac{3}{4}\right)^{2}$$

Multiply 125 and -1 to get -125.

$$500x+\frac{-125}{8}+\left(\frac{3}{4}\right)^{2}$$

Fraction \frac{-125}{8} can be rewritten as -\frac{125}{8} by extracting the negative sign.

$$500x-\frac{125}{8}+\left(\frac{3}{4}\right)^{2}$$

Calculate \frac{3}{4} to the power of 2 and get \frac{9}{16}.

$$500x-\frac{125}{8}+\frac{9}{16}$$

Least common multiple of 8 and 16 is 16. Convert -\frac{125}{8} and \frac{9}{16} to fractions with denominator 16.

$$500x-\frac{250}{16}+\frac{9}{16}$$

Since -\frac{250}{16} and \frac{9}{16} have the same denominator, add them by adding their numerators.

$$500x+\frac{-250+9}{16}$$

Add -250 and 9 to get -241.

$$500x-\frac{241}{16}$$