Solve =(2-3x)(1/7+2/5x)+(x-2/11x)(x^2-5x-1/5)-(frac{3x-7}{3})^2

$$= ( 2 - 3 x ) ( \frac { 1 } { 7 } + \frac { 2 } { 5 } x ) + ( x - \frac { 2 } { 11 } x ) ( x ^ { 2 } - 5 x - \frac { 1 } { 5 } ) - ( \frac { 3 x - 7 } { 3 } ) ^ { 2 }$$

Evaluate

$$\frac{9x^{3}}{11}-\frac{346x^{2}}{55}+\frac{1126x}{231}-\frac{325}{63}$$

Short Solution Steps

Use the distributive property to multiply 2-3x by \frac{1}{7}+\frac{2}{5}x and combine like terms.

$$\frac{2}{7}+\frac{13}{35}x-\frac{6}{5}x^{2}+\left(x-\frac{2}{11}x\right)\left(x^{2}-5x-\frac{1}{5}\right)-\left(\frac{3x-7}{3}\right)^{2}$$

Combine x and -\frac{2}{11}x to get \frac{9}{11}x.

$$\frac{2}{7}+\frac{13}{35}x-\frac{6}{5}x^{2}+\frac{9}{11}x\left(x^{2}-5x-\frac{1}{5}\right)-\left(\frac{3x-7}{3}\right)^{2}$$

Use the distributive property to multiply \frac{9}{11}x by x^{2}-5x-\frac{1}{5}.

$$\frac{2}{7}+\frac{13}{35}x-\frac{6}{5}x^{2}+\frac{9}{11}x^{3}-\frac{45}{11}x^{2}-\frac{9}{55}x-\left(\frac{3x-7}{3}\right)^{2}$$

Combine -\frac{6}{5}x^{2} and -\frac{45}{11}x^{2} to get -\frac{291}{55}x^{2}.

$$\frac{2}{7}+\frac{13}{35}x-\frac{291}{55}x^{2}+\frac{9}{11}x^{3}-\frac{9}{55}x-\left(\frac{3x-7}{3}\right)^{2}$$

Combine \frac{13}{35}x and -\frac{9}{55}x to get \frac{16}{77}x.

$$\frac{2}{7}+\frac{16}{77}x-\frac{291}{55}x^{2}+\frac{9}{11}x^{3}-\left(\frac{3x-7}{3}\right)^{2}$$

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

$$\frac{2}{7}+\frac{16}{77}x-\frac{291}{55}x^{2}+\frac{9}{11}x^{3}-\frac{\left(3x-7\right)^{2}}{3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{2}{7}+\frac{16}{77}x-\frac{291}{55}x^{2}+\frac{9}{11}x^{3}-\frac{\left(3x-7\right)^{2}}{9}$$

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

$$\frac{2\times 9}{63}+\frac{16}{77}x-\frac{291}{55}x^{2}+\frac{9}{11}x^{3}-\frac{7\left(3x-7\right)^{2}}{63}$$

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

$$\frac{2\times 9-7\left(3x-7\right)^{2}}{63}+\frac{16}{77}x-\frac{291}{55}x^{2}+\frac{9}{11}x^{3}$$

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

$$\frac{18-63x^{2}+294x-343}{63}+\frac{16}{77}x-\frac{291}{55}x^{2}+\frac{9}{11}x^{3}$$

Combine like terms in 18-63x^{2}+294x-343.

$$\frac{-325-63x^{2}+294x}{63}+\frac{16}{77}x-\frac{291}{55}x^{2}+\frac{9}{11}x^{3}$$

Divide each term of -325-63x^{2}+294x by 63 to get -\frac{325}{63}+\frac{14}{3}x-x^{2}.

$$-\frac{325}{63}+\frac{14}{3}x-x^{2}+\frac{16}{77}x-\frac{291}{55}x^{2}+\frac{9}{11}x^{3}$$

Combine \frac{14}{3}x and \frac{16}{77}x to get \frac{1126}{231}x.

$$-\frac{325}{63}+\frac{1126}{231}x-x^{2}-\frac{291}{55}x^{2}+\frac{9}{11}x^{3}$$

Combine -x^{2} and -\frac{291}{55}x^{2} to get -\frac{346}{55}x^{2}.

$$-\frac{325}{63}+\frac{1126}{231}x-\frac{346}{55}x^{2}+\frac{9}{11}x^{3}$$

Expand

$$\frac{9x^{3}}{11}-\frac{346x^{2}}{55}+\frac{1126x}{231}-\frac{325}{63}$$

Short Solution Steps

Use the distributive property to multiply 2-3x by \frac{1}{7}+\frac{2}{5}x and combine like terms.

$$\frac{2}{7}+\frac{13}{35}x-\frac{6}{5}x^{2}+\left(x-\frac{2}{11}x\right)\left(x^{2}-5x-\frac{1}{5}\right)-\left(\frac{3x-7}{3}\right)^{2}$$

Combine x and -\frac{2}{11}x to get \frac{9}{11}x.

$$\frac{2}{7}+\frac{13}{35}x-\frac{6}{5}x^{2}+\frac{9}{11}x\left(x^{2}-5x-\frac{1}{5}\right)-\left(\frac{3x-7}{3}\right)^{2}$$

Use the distributive property to multiply \frac{9}{11}x by x^{2}-5x-\frac{1}{5}.

$$\frac{2}{7}+\frac{13}{35}x-\frac{6}{5}x^{2}+\frac{9}{11}x^{3}-\frac{45}{11}x^{2}-\frac{9}{55}x-\left(\frac{3x-7}{3}\right)^{2}$$

Combine -\frac{6}{5}x^{2} and -\frac{45}{11}x^{2} to get -\frac{291}{55}x^{2}.

$$\frac{2}{7}+\frac{13}{35}x-\frac{291}{55}x^{2}+\frac{9}{11}x^{3}-\frac{9}{55}x-\left(\frac{3x-7}{3}\right)^{2}$$

Combine \frac{13}{35}x and -\frac{9}{55}x to get \frac{16}{77}x.

$$\frac{2}{7}+\frac{16}{77}x-\frac{291}{55}x^{2}+\frac{9}{11}x^{3}-\left(\frac{3x-7}{3}\right)^{2}$$

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

$$\frac{2}{7}+\frac{16}{77}x-\frac{291}{55}x^{2}+\frac{9}{11}x^{3}-\frac{\left(3x-7\right)^{2}}{3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{2}{7}+\frac{16}{77}x-\frac{291}{55}x^{2}+\frac{9}{11}x^{3}-\frac{\left(3x-7\right)^{2}}{9}$$

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

$$\frac{2\times 9}{63}+\frac{16}{77}x-\frac{291}{55}x^{2}+\frac{9}{11}x^{3}-\frac{7\left(3x-7\right)^{2}}{63}$$

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

$$\frac{2\times 9-7\left(3x-7\right)^{2}}{63}+\frac{16}{77}x-\frac{291}{55}x^{2}+\frac{9}{11}x^{3}$$

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

$$\frac{18-63x^{2}+294x-343}{63}+\frac{16}{77}x-\frac{291}{55}x^{2}+\frac{9}{11}x^{3}$$

Combine like terms in 18-63x^{2}+294x-343.

$$\frac{-325-63x^{2}+294x}{63}+\frac{16}{77}x-\frac{291}{55}x^{2}+\frac{9}{11}x^{3}$$

Divide each term of -325-63x^{2}+294x by 63 to get -\frac{325}{63}+\frac{14}{3}x-x^{2}.

$$-\frac{325}{63}+\frac{14}{3}x-x^{2}+\frac{16}{77}x-\frac{291}{55}x^{2}+\frac{9}{11}x^{3}$$

Combine \frac{14}{3}x and \frac{16}{77}x to get \frac{1126}{231}x.

$$-\frac{325}{63}+\frac{1126}{231}x-x^{2}-\frac{291}{55}x^{2}+\frac{9}{11}x^{3}$$

Combine -x^{2} and -\frac{291}{55}x^{2} to get -\frac{346}{55}x^{2}.

$$-\frac{325}{63}+\frac{1126}{231}x-\frac{346}{55}x^{2}+\frac{9}{11}x^{3}$$