What is ((2t)/5-(w^2)/4)((2t)/5+(w^2)/4) ?

The solution to ((2t)/5-(w^2)/4)((2t)/5+(w^2)/4) is ((8t-5w^2)(8t+5w^2))/(400)

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simplify ((2t)/5-(w^2)/4)((2t)/5+(w^2)/4)

simplify

(\frac{2 t}{5} - \frac{w ^{2}}{4}) (\frac{2 t}{5} + \frac{w ^{2}}{4})

\frac{( 8 t - 5 w ^{2} ) ( 8 t + 5 w ^{2} )}{400}

Solution steps

(\frac{2 t}{5} - \frac{w ^{2}}{4}) (\frac{2 t}{5} + \frac{w ^{2}}{4})

Simplify

\frac{2 t}{5} - \frac{w ^{2}}{4} : \frac{8 t - 5 w ^{2}}{20}

= \frac{8 t - 5 w ^{2}}{20} (\frac{2 t}{5} + \frac{w ^{2}}{4})

Apply the fraction rule:

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

= \frac{( 8 t - 5 w ^{2} ) ( \frac{2 t}{5} + \frac{w ^{2}}{4} )}{20}

Simplify

(8 t - 5 w^{2}) (\frac{2 t}{5} + \frac{w ^{2}}{4}) : \frac{( 8 t - 5 w ^{2} ) ( 8 t + w ^{2} \cdot 5 )}{20}

= \frac{\frac{( 8 t - 5 w ^{2} ) ( 8 t + w ^{2} \cdot 5 )}{20}}{20}

Apply the fraction rule:

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

= \frac{( 8 t - 5 w ^{2} ) ( 8 t + w ^{2} \cdot 5 )}{20 \cdot 20}

Multiply the numbers:

20 \cdot 20 = 400

= \frac{( 8 t - 5 w ^{2} ) ( 8 t + w ^{2} \cdot 5 )}{400}

= \frac{( 8 t - 5 w ^{2} ) ( 8 t + 5 w ^{2} )}{400}

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What is ((2t)/5-(w^2)/4)((2t)/5+(w^2)/4) ?
The solution to ((2t)/5-(w^2)/4)((2t)/5+(w^2)/4) is ((8t-5w^2)(8t+5w^2))/(400)