Solve -3/7(3/7+7)+(3/7+5)(3/7-5)

$$- \frac { 3 } { 7 } ( \frac { 3 } { 7 } + 7 ) + ( \frac { 3 } { 7 } + 5 ) ( \frac { 3 } { 7 } - 5 )$$

Evaluate

$$-28$$

Solution Steps

Convert 7 to fraction \frac{49}{7}.

$$-\frac{3}{7}\left(\frac{3}{7}+\frac{49}{7}\right)+\left(\frac{3}{7}+5\right)\left(\frac{3}{7}-5\right)$$

Since \frac{3}{7} and \frac{49}{7} have the same denominator, add them by adding their numerators.

$$-\frac{3}{7}\times \frac{3+49}{7}+\left(\frac{3}{7}+5\right)\left(\frac{3}{7}-5\right)$$

Add 3 and 49 to get 52.

$$-\frac{3}{7}\times \frac{52}{7}+\left(\frac{3}{7}+5\right)\left(\frac{3}{7}-5\right)$$

Multiply -\frac{3}{7} times \frac{52}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-3\times 52}{7\times 7}+\left(\frac{3}{7}+5\right)\left(\frac{3}{7}-5\right)$$

Do the multiplications in the fraction \frac{-3\times 52}{7\times 7}.

$$\frac{-156}{49}+\left(\frac{3}{7}+5\right)\left(\frac{3}{7}-5\right)$$

Fraction \frac{-156}{49} can be rewritten as -\frac{156}{49} by extracting the negative sign.

$$-\frac{156}{49}+\left(\frac{3}{7}+5\right)\left(\frac{3}{7}-5\right)$$

Convert 5 to fraction \frac{35}{7}.

$$-\frac{156}{49}+\left(\frac{3}{7}+\frac{35}{7}\right)\left(\frac{3}{7}-5\right)$$

Since \frac{3}{7} and \frac{35}{7} have the same denominator, add them by adding their numerators.

$$-\frac{156}{49}+\frac{3+35}{7}\left(\frac{3}{7}-5\right)$$

Add 3 and 35 to get 38.

$$-\frac{156}{49}+\frac{38}{7}\left(\frac{3}{7}-5\right)$$

Convert 5 to fraction \frac{35}{7}.

$$-\frac{156}{49}+\frac{38}{7}\left(\frac{3}{7}-\frac{35}{7}\right)$$

Since \frac{3}{7} and \frac{35}{7} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{156}{49}+\frac{38}{7}\times \frac{3-35}{7}$$

Subtract 35 from 3 to get -32.

$$-\frac{156}{49}+\frac{38}{7}\left(-\frac{32}{7}\right)$$

Multiply \frac{38}{7} times -\frac{32}{7} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{156}{49}+\frac{38\left(-32\right)}{7\times 7}$$

Do the multiplications in the fraction \frac{38\left(-32\right)}{7\times 7}.

$$-\frac{156}{49}+\frac{-1216}{49}$$

Fraction \frac{-1216}{49} can be rewritten as -\frac{1216}{49} by extracting the negative sign.

$$-\frac{156}{49}-\frac{1216}{49}$$

Since -\frac{156}{49} and \frac{1216}{49} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-156-1216}{49}$$

Subtract 1216 from -156 to get -1372.

$$\frac{-1372}{49}$$

Divide -1372 by 49 to get -28.

$$-28$$

Factor

$$-28$$