What is (16x^8-625y^4)/(2x^2+5y) ?

The solution to (16x^8-625y^4)/(2x^2+5y) is (4x^4+25y^2)(2x^2-5y)

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simplify (16x^8-625y^4)/(2x^2+5y)

simplify

\frac{16 x ^{8} - 625 y ^{4}}{2 x ^{2} + 5 y}

(4 x^{4} + 25 y^{2}) (2 x^{2} - 5 y)

Solution steps

\frac{16 x ^{8} - 625 y ^{4}}{2 x ^{2} + 5 y}

16 x^{8} = (4 x^{4})^{2}

625 y^{4} = (25 y^{2})^{2}

= \frac{( 4 x ^{4} ) ^{2} - ( 25 y ^{2} ) ^{2}}{2 x ^{2} + 5 y}

Apply Difference of Two Squares Formula:

x^{2} - y^{2} = (x + y) (x - y)

(4 x^{4})^{2} - (25 y^{2})^{2} = (4 x^{4} + 25 y^{2}) (4 x^{4} - 25 y^{2})

= \frac{( 4 x ^{4} + 25 y ^{2} ) ( 4 x ^{4} - 25 y ^{2} )}{2 x ^{2} + 5 y}

Factor

4 x^{4} - 25 y^{2} : (2 x^{2} + 5 y) (2 x^{2} - 5 y)

= \frac{( 4 x ^{4} + 25 y ^{2} ) ( 2 x ^{2} + 5 y ) ( 2 x ^{2} - 5 y )}{2 x ^{2} + 5 y}

Cancel the common factor:

2 x^{2} + 5 y

= (4 x^{4} + 25 y^{2}) (2 x^{2} - 5 y)

\frac{7}{m} \cdot \frac{m + 7}{14}

(\frac{3}{2} y - \frac{1}{3} x) (- \frac{4}{5} x - \frac{1}{2} y)

3 x^{3} - 12 x^{2} + 2 x - 8

\frac{6 z ^{9}}{3 ( z ) ^{2}}

5 \cdot (- 2 w - 4)

What is (16x^8-625y^4)/(2x^2+5y) ?
The solution to (16x^8-625y^4)/(2x^2+5y) is (4x^4+25y^2)(2x^2-5y)