What is (8a^3+27)/(4a^2+12a+9) ?

The solution to (8a^3+27)/(4a^2+12a+9) is (4a^2-6a+9)/(2a+3)

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simplify (8a^3+27)/(4a^2+12a+9)

simplify

\frac{8 a ^{3} + 27}{4 a ^{2} + 12 a + 9}

\frac{4 a ^{2} - 6 a + 9}{2 a + 3}

Solution steps

\frac{8 a ^{3} + 27}{4 a ^{2} + 12 a + 9}

Factor

8 a^{3} + 27 : (2 a + 3) (4 a^{2} - 6 a + 9)

= \frac{( 2 a + 3 ) ( 4 a ^{2} - 6 a + 9 )}{4 a ^{2} + 12 a + 9}

Factor

4 a^{2} + 12 a + 9 : (2 a + 3)^{2}

= \frac{( 2 a + 3 ) ( 4 a ^{2} - 6 a + 9 )}{( 2 a + 3 ) ^{2}}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(2 a + 3)^{2} = (2 a + 3) (2 a + 3)

= \frac{( 2 a + 3 ) ( 4 a ^{2} - 6 a + 9 )}{( 2 a + 3 ) ( 2 a + 3 )}

Cancel the common factor:

2 a + 3

= \frac{4 a ^{2} - 6 a + 9}{2 a + 3}

\frac{cos ( x )}{sin ( x )} + \frac{sin ( x )}{1 + cos ( x )}

(3^{- 1} + 3^{- 2})^{- 1}

(5 x y + 14 x + 6 y) - (8 x - 4 y + 2 x y)

3 + \frac{1}{3} - \frac{1}{12} - (1 - (2 \frac{1}{4} + 1.7))

\frac{3 x ^{2} y z ^{4}}{6 x y z ^{2}} \cdot \frac{2 x ^{2} y ^{4}}{6 x y ^{3}}

What is (8a^3+27)/(4a^2+12a+9) ?
The solution to (8a^3+27)/(4a^2+12a+9) is (4a^2-6a+9)/(2a+3)