Solve (1/7+2/5x)+(x-2/1x)(x^2-5x-1/5)-(frac{3x-7}{3})^2

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

Evaluate

$$-x^{3}+4x^{2}+\frac{79x}{15}-\frac{334}{63}$$

Short Solution Steps

Anything divided by one gives itself.

$$\frac{1}{7}+\frac{2}{5}x+\left(x-2x\right)\left(x^{2}-5x-\frac{1}{5}\right)-\left(\frac{3x-7}{3}\right)^{2}$$

Combine x and -2x to get -x.

$$\frac{1}{7}+\frac{2}{5}x-x\left(x^{2}-5x-\frac{1}{5}\right)-\left(\frac{3x-7}{3}\right)^{2}$$

Use the distributive property to multiply -x by x^{2}-5x-\frac{1}{5}.

$$\frac{1}{7}+\frac{2}{5}x-x^{3}+5x^{2}+\frac{1}{5}x-\left(\frac{3x-7}{3}\right)^{2}$$

Combine \frac{2}{5}x and \frac{1}{5}x to get \frac{3}{5}x.

$$\frac{1}{7}+\frac{3}{5}x-x^{3}+5x^{2}-\left(\frac{3x-7}{3}\right)^{2}$$

To raise \frac{3x-7}{3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1}{7}+\frac{3}{5}x-x^{3}+5x^{2}-\frac{\left(3x-7\right)^{2}}{3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{1}{7}+\frac{3}{5}x-x^{3}+5x^{2}-\frac{\left(3x-7\right)^{2}}{9}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 7 and 9 is 63. Multiply \frac{1}{7} times \frac{9}{9}. Multiply \frac{\left(3x-7\right)^{2}}{9} times \frac{7}{7}.

$$\frac{9}{63}+\frac{3}{5}x-x^{3}+5x^{2}-\frac{7\left(3x-7\right)^{2}}{63}$$

Since \frac{9}{63} and \frac{7\left(3x-7\right)^{2}}{63} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-7\left(3x-7\right)^{2}}{63}+\frac{3}{5}x-x^{3}+5x^{2}$$

Do the multiplications in 9-7\left(3x-7\right)^{2}.

$$\frac{9-63x^{2}+294x-343}{63}+\frac{3}{5}x-x^{3}+5x^{2}$$

Combine like terms in 9-63x^{2}+294x-343.

$$\frac{-334-63x^{2}+294x}{63}+\frac{3}{5}x-x^{3}+5x^{2}$$

Divide each term of -334-63x^{2}+294x by 63 to get -\frac{334}{63}-x^{2}+\frac{14}{3}x.

$$-\frac{334}{63}-x^{2}+\frac{14}{3}x+\frac{3}{5}x-x^{3}+5x^{2}$$

Combine \frac{14}{3}x and \frac{3}{5}x to get \frac{79}{15}x.

$$-\frac{334}{63}-x^{2}+\frac{79}{15}x-x^{3}+5x^{2}$$

Combine -x^{2} and 5x^{2} to get 4x^{2}.

$$-\frac{334}{63}+4x^{2}+\frac{79}{15}x-x^{3}$$

Expand

$$-x^{3}+4x^{2}+\frac{79x}{15}-\frac{334}{63}$$

Short Solution Steps

Anything divided by one gives itself.

$$\frac{1}{7}+\frac{2}{5}x+\left(x-2x\right)\left(x^{2}-5x-\frac{1}{5}\right)-\left(\frac{3x-7}{3}\right)^{2}$$

Combine x and -2x to get -x.

$$\frac{1}{7}+\frac{2}{5}x-x\left(x^{2}-5x-\frac{1}{5}\right)-\left(\frac{3x-7}{3}\right)^{2}$$

Use the distributive property to multiply -x by x^{2}-5x-\frac{1}{5}.

$$\frac{1}{7}+\frac{2}{5}x-x^{3}+5x^{2}+\frac{1}{5}x-\left(\frac{3x-7}{3}\right)^{2}$$

Combine \frac{2}{5}x and \frac{1}{5}x to get \frac{3}{5}x.

$$\frac{1}{7}+\frac{3}{5}x-x^{3}+5x^{2}-\left(\frac{3x-7}{3}\right)^{2}$$

To raise \frac{3x-7}{3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1}{7}+\frac{3}{5}x-x^{3}+5x^{2}-\frac{\left(3x-7\right)^{2}}{3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{1}{7}+\frac{3}{5}x-x^{3}+5x^{2}-\frac{\left(3x-7\right)^{2}}{9}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 7 and 9 is 63. Multiply \frac{1}{7} times \frac{9}{9}. Multiply \frac{\left(3x-7\right)^{2}}{9} times \frac{7}{7}.

$$\frac{9}{63}+\frac{3}{5}x-x^{3}+5x^{2}-\frac{7\left(3x-7\right)^{2}}{63}$$

Since \frac{9}{63} and \frac{7\left(3x-7\right)^{2}}{63} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-7\left(3x-7\right)^{2}}{63}+\frac{3}{5}x-x^{3}+5x^{2}$$

Do the multiplications in 9-7\left(3x-7\right)^{2}.

$$\frac{9-63x^{2}+294x-343}{63}+\frac{3}{5}x-x^{3}+5x^{2}$$

Combine like terms in 9-63x^{2}+294x-343.

$$\frac{-334-63x^{2}+294x}{63}+\frac{3}{5}x-x^{3}+5x^{2}$$

Divide each term of -334-63x^{2}+294x by 63 to get -\frac{334}{63}-x^{2}+\frac{14}{3}x.

$$-\frac{334}{63}-x^{2}+\frac{14}{3}x+\frac{3}{5}x-x^{3}+5x^{2}$$

Combine \frac{14}{3}x and \frac{3}{5}x to get \frac{79}{15}x.

$$-\frac{334}{63}-x^{2}+\frac{79}{15}x-x^{3}+5x^{2}$$

Combine -x^{2} and 5x^{2} to get 4x^{2}.

$$-\frac{334}{63}+4x^{2}+\frac{79}{15}x-x^{3}$$