Solve 4/7(2a+9)-2/3(3a+7)*3/14(5a-10)

$$\frac { 4 } { 7 } ( 2 a + 9 ) - \frac { 2 } { 3 } ( 3 a + 7 ) \cdot \frac { 3 } { 14 } ( 5 a - 10 )$$

Evaluate

$$\frac{106+3a-15a^{2}}{7}$$

Solution Steps

Use the distributive property to multiply \frac{4}{7} by 2a+9.

$$\frac{4}{7}\times 2a+\frac{4}{7}\times 9-\frac{2}{3}\left(3a+7\right)\times \frac{3}{14}\left(5a-10\right)$$

Express \frac{4}{7}\times 2 as a single fraction.

$$\frac{4\times 2}{7}a+\frac{4}{7}\times 9-\frac{2}{3}\left(3a+7\right)\times \frac{3}{14}\left(5a-10\right)$$

Multiply 4 and 2 to get 8.

$$\frac{8}{7}a+\frac{4}{7}\times 9-\frac{2}{3}\left(3a+7\right)\times \frac{3}{14}\left(5a-10\right)$$

Express \frac{4}{7}\times 9 as a single fraction.

$$\frac{8}{7}a+\frac{4\times 9}{7}-\frac{2}{3}\left(3a+7\right)\times \frac{3}{14}\left(5a-10\right)$$

Multiply 4 and 9 to get 36.

$$\frac{8}{7}a+\frac{36}{7}-\frac{2}{3}\left(3a+7\right)\times \frac{3}{14}\left(5a-10\right)$$

Multiply \frac{2}{3} times \frac{3}{14} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8}{7}a+\frac{36}{7}-\frac{2\times 3}{3\times 14}\left(3a+7\right)\left(5a-10\right)$$

Cancel out 3 in both numerator and denominator.

$$\frac{8}{7}a+\frac{36}{7}-\frac{2}{14}\left(3a+7\right)\left(5a-10\right)$$

Reduce the fraction \frac{2}{14} to lowest terms by extracting and canceling out 2.

$$\frac{8}{7}a+\frac{36}{7}-\frac{1}{7}\left(3a+7\right)\left(5a-10\right)$$

Use the distributive property to multiply -\frac{1}{7} by 3a+7.

$$\frac{8}{7}a+\frac{36}{7}+\left(-\frac{1}{7}\times 3a-\frac{1}{7}\times 7\right)\left(5a-10\right)$$

Express -\frac{1}{7}\times 3 as a single fraction.

$$\frac{8}{7}a+\frac{36}{7}+\left(\frac{-3}{7}a-\frac{1}{7}\times 7\right)\left(5a-10\right)$$

Fraction \frac{-3}{7} can be rewritten as -\frac{3}{7} by extracting the negative sign.

$$\frac{8}{7}a+\frac{36}{7}+\left(-\frac{3}{7}a-\frac{1}{7}\times 7\right)\left(5a-10\right)$$

Cancel out 7 and 7.

$$\frac{8}{7}a+\frac{36}{7}+\left(-\frac{3}{7}a-1\right)\left(5a-10\right)$$

Apply the distributive property by multiplying each term of -\frac{3}{7}a-1 by each term of 5a-10.

$$\frac{8}{7}a+\frac{36}{7}-\frac{3}{7}a\times 5a-\frac{3}{7}a\left(-10\right)-5a+10$$

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

$$\frac{8}{7}a+\frac{36}{7}-\frac{3}{7}a^{2}\times 5-\frac{3}{7}a\left(-10\right)-5a+10$$

Express -\frac{3}{7}\times 5 as a single fraction.

$$\frac{8}{7}a+\frac{36}{7}+\frac{-3\times 5}{7}a^{2}-\frac{3}{7}a\left(-10\right)-5a+10$$

Multiply -3 and 5 to get -15.

$$\frac{8}{7}a+\frac{36}{7}+\frac{-15}{7}a^{2}-\frac{3}{7}a\left(-10\right)-5a+10$$

Fraction \frac{-15}{7} can be rewritten as -\frac{15}{7} by extracting the negative sign.

$$\frac{8}{7}a+\frac{36}{7}-\frac{15}{7}a^{2}-\frac{3}{7}a\left(-10\right)-5a+10$$

Express -\frac{3}{7}\left(-10\right) as a single fraction.

$$\frac{8}{7}a+\frac{36}{7}-\frac{15}{7}a^{2}+\frac{-3\left(-10\right)}{7}a-5a+10$$

Multiply -3 and -10 to get 30.

$$\frac{8}{7}a+\frac{36}{7}-\frac{15}{7}a^{2}+\frac{30}{7}a-5a+10$$

Combine \frac{30}{7}a and -5a to get -\frac{5}{7}a.

$$\frac{8}{7}a+\frac{36}{7}-\frac{15}{7}a^{2}-\frac{5}{7}a+10$$

Combine \frac{8}{7}a and -\frac{5}{7}a to get \frac{3}{7}a.

$$\frac{3}{7}a+\frac{36}{7}-\frac{15}{7}a^{2}+10$$

Convert 10 to fraction \frac{70}{7}.

$$\frac{3}{7}a+\frac{36}{7}-\frac{15}{7}a^{2}+\frac{70}{7}$$

Since \frac{36}{7} and \frac{70}{7} have the same denominator, add them by adding their numerators.

$$\frac{3}{7}a+\frac{36+70}{7}-\frac{15}{7}a^{2}$$

Add 36 and 70 to get 106.

$$\frac{3}{7}a+\frac{106}{7}-\frac{15}{7}a^{2}$$

Expand

$$\frac{106+3a-15a^{2}}{7}$$

Solution Steps

Use the distributive property to multiply \frac{4}{7} by 2a+9.

$$\frac{4}{7}\times 2a+\frac{4}{7}\times 9-\frac{2}{3}\left(3a+7\right)\times \frac{3}{14}\left(5a-10\right)$$

Express \frac{4}{7}\times 2 as a single fraction.

$$\frac{4\times 2}{7}a+\frac{4}{7}\times 9-\frac{2}{3}\left(3a+7\right)\times \frac{3}{14}\left(5a-10\right)$$

Multiply 4 and 2 to get 8.

$$\frac{8}{7}a+\frac{4}{7}\times 9-\frac{2}{3}\left(3a+7\right)\times \frac{3}{14}\left(5a-10\right)$$

Express \frac{4}{7}\times 9 as a single fraction.

$$\frac{8}{7}a+\frac{4\times 9}{7}-\frac{2}{3}\left(3a+7\right)\times \frac{3}{14}\left(5a-10\right)$$

Multiply 4 and 9 to get 36.

$$\frac{8}{7}a+\frac{36}{7}-\frac{2}{3}\left(3a+7\right)\times \frac{3}{14}\left(5a-10\right)$$

Multiply \frac{2}{3} times \frac{3}{14} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8}{7}a+\frac{36}{7}-\frac{2\times 3}{3\times 14}\left(3a+7\right)\left(5a-10\right)$$

Cancel out 3 in both numerator and denominator.

$$\frac{8}{7}a+\frac{36}{7}-\frac{2}{14}\left(3a+7\right)\left(5a-10\right)$$

Reduce the fraction \frac{2}{14} to lowest terms by extracting and canceling out 2.

$$\frac{8}{7}a+\frac{36}{7}-\frac{1}{7}\left(3a+7\right)\left(5a-10\right)$$

Use the distributive property to multiply -\frac{1}{7} by 3a+7.

$$\frac{8}{7}a+\frac{36}{7}+\left(-\frac{1}{7}\times 3a-\frac{1}{7}\times 7\right)\left(5a-10\right)$$

Express -\frac{1}{7}\times 3 as a single fraction.

$$\frac{8}{7}a+\frac{36}{7}+\left(\frac{-3}{7}a-\frac{1}{7}\times 7\right)\left(5a-10\right)$$

Fraction \frac{-3}{7} can be rewritten as -\frac{3}{7} by extracting the negative sign.

$$\frac{8}{7}a+\frac{36}{7}+\left(-\frac{3}{7}a-\frac{1}{7}\times 7\right)\left(5a-10\right)$$

Cancel out 7 and 7.

$$\frac{8}{7}a+\frac{36}{7}+\left(-\frac{3}{7}a-1\right)\left(5a-10\right)$$

Apply the distributive property by multiplying each term of -\frac{3}{7}a-1 by each term of 5a-10.

$$\frac{8}{7}a+\frac{36}{7}-\frac{3}{7}a\times 5a-\frac{3}{7}a\left(-10\right)-5a+10$$

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

$$\frac{8}{7}a+\frac{36}{7}-\frac{3}{7}a^{2}\times 5-\frac{3}{7}a\left(-10\right)-5a+10$$

Express -\frac{3}{7}\times 5 as a single fraction.

$$\frac{8}{7}a+\frac{36}{7}+\frac{-3\times 5}{7}a^{2}-\frac{3}{7}a\left(-10\right)-5a+10$$

Multiply -3 and 5 to get -15.

$$\frac{8}{7}a+\frac{36}{7}+\frac{-15}{7}a^{2}-\frac{3}{7}a\left(-10\right)-5a+10$$

Fraction \frac{-15}{7} can be rewritten as -\frac{15}{7} by extracting the negative sign.

$$\frac{8}{7}a+\frac{36}{7}-\frac{15}{7}a^{2}-\frac{3}{7}a\left(-10\right)-5a+10$$

Express -\frac{3}{7}\left(-10\right) as a single fraction.

$$\frac{8}{7}a+\frac{36}{7}-\frac{15}{7}a^{2}+\frac{-3\left(-10\right)}{7}a-5a+10$$

Multiply -3 and -10 to get 30.

$$\frac{8}{7}a+\frac{36}{7}-\frac{15}{7}a^{2}+\frac{30}{7}a-5a+10$$

Combine \frac{30}{7}a and -5a to get -\frac{5}{7}a.

$$\frac{8}{7}a+\frac{36}{7}-\frac{15}{7}a^{2}-\frac{5}{7}a+10$$

Combine \frac{8}{7}a and -\frac{5}{7}a to get \frac{3}{7}a.

$$\frac{3}{7}a+\frac{36}{7}-\frac{15}{7}a^{2}+10$$

Convert 10 to fraction \frac{70}{7}.

$$\frac{3}{7}a+\frac{36}{7}-\frac{15}{7}a^{2}+\frac{70}{7}$$

Since \frac{36}{7} and \frac{70}{7} have the same denominator, add them by adding their numerators.

$$\frac{3}{7}a+\frac{36+70}{7}-\frac{15}{7}a^{2}$$

Add 36 and 70 to get 106.

$$\frac{3}{7}a+\frac{106}{7}-\frac{15}{7}a^{2}$$