What is (8m^3+64)/(4m^2+34m+52) ?

The solution to (8m^3+64)/(4m^2+34m+52) is (4(m^2-2m+4))/(2m+13)

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simplify (8m^3+64)/(4m^2+34m+52)

simplify

\frac{8 m ^{3} + 64}{4 m ^{2} + 34 m + 52}

\frac{4 ( m ^{2} - 2 m + 4 )}{2 m + 13}

Solution steps

\frac{8 m ^{3} + 64}{4 m ^{2} + 34 m + 52}

Factor

8 m^{3} + 64 : 8 (m + 2) (m^{2} - 2 m + 4)

= \frac{8 ( m + 2 ) ( m ^{2} - 2 m + 4 )}{4 m ^{2} + 34 m + 52}

Factor

4 m^{2} + 34 m + 52 : 2 (m + 2) (2 m + 13)

= \frac{8 ( m + 2 ) ( m ^{2} - 2 m + 4 )}{2 ( m + 2 ) ( 2 m + 13 )}

Cancel the common factor:

m + 2

= \frac{8 ( m ^{2} - 2 m + 4 )}{2 ( 2 m + 13 )}

Factor the number:

8 = 2 \cdot 4

= \frac{2 \cdot 4 ( m ^{2} - 2 m + 4 )}{2 ( 2 m + 13 )}

Cancel the common factor:

2

= \frac{4 ( m ^{2} - 2 m + 4 )}{2 m + 13}

- \frac{x}{4} - 2 = x + 3

- 6 - 3 (1 + 5 n) = 33 - 8 n

x^{2} = 9 2^{2} + 9 2^{2}

4 x^{2} - 56 x + 189 > 0

3 = - 4 x

What is (8m^3+64)/(4m^2+34m+52) ?
The solution to (8m^3+64)/(4m^2+34m+52) is (4(m^2-2m+4))/(2m+13)