What is ((a^2b)/3-(2c)/5)((a^2b)/3+(2c)/5) ?

The solution to ((a^2b)/3-(2c)/5)((a^2b)/3+(2c)/5) is ((5a^2b-6c)(5a^2b+6c))/(225)

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simplify ((a^2b)/3-(2c)/5)((a^2b)/3+(2c)/5)

simplify

(\frac{a ^{2} b}{3} - \frac{2 c}{5}) (\frac{a ^{2} b}{3} + \frac{2 c}{5})

\frac{( 5 a ^{2} b - 6 c ) ( 5 a ^{2} b + 6 c )}{225}

Solution steps

(\frac{a ^{2} b}{3} - \frac{2 c}{5}) (\frac{a ^{2} b}{3} + \frac{2 c}{5})

Simplify

\frac{a ^{2} b}{3} - \frac{2 c}{5} : \frac{5 a ^{2} b - 6 c}{15}

= \frac{5 a ^{2} b - 6 c}{15} (\frac{a ^{2} b}{3} + \frac{2 c}{5})

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{( 5 a ^{2} b - 6 c ) ( \frac{a ^{2} b}{3} + \frac{2 c}{5} )}{15}

Simplify

(5 a^{2} b - 6 c) (\frac{a ^{2} b}{3} + \frac{2 c}{5}) : \frac{( 5 a ^{2} b - 6 c ) ( a ^{2} b \cdot 5 + 6 c )}{15}

= \frac{\frac{( 5 a ^{2} b - 6 c ) ( a ^{2} b \cdot 5 + 6 c )}{15}}{15}

Apply the fraction rule:

\frac{\frac{a}{b}}{c} = \frac{a}{b \cdot c}

= \frac{( 5 a ^{2} b - 6 c ) ( a ^{2} b \cdot 5 + 6 c )}{15 \cdot 15}

Multiply the numbers:

15 \cdot 15 = 225

= \frac{( 5 a ^{2} b - 6 c ) ( a ^{2} b \cdot 5 + 6 c )}{225}

= \frac{( 5 a ^{2} b - 6 c ) ( 5 a ^{2} b + 6 c )}{225}

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What is ((a^2b)/3-(2c)/5)((a^2b)/3+(2c)/5) ?
The solution to ((a^2b)/3-(2c)/5)((a^2b)/3+(2c)/5) is ((5a^2b-6c)(5a^2b+6c))/(225)