What is factor 8a^6+27b^9 ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

factor 8a^6+27b^9

factor

8 a^{6} + 27 b^{9}

(2 a^{2} + 3 b^{3}) (4 a^{4} - 6 a^{2} b^{3} + 9 b^{6})

Solution steps

8 a^{6} + 27 b^{9}

Apply exponent rules

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

Apply Sum of Cubes Formula:

x^{3} + y^{3} = (x + y) (x^{2} - x y + y^{2})

(2 a^{2})^{3} + (3 b^{3})^{3} = (2 a^{2} + 3 b^{3}) ((2 a^{2})^{2} - 2 a^{2} \cdot 3 b^{3} + (3 b^{3})^{2})

= (2 a^{2} + 3 b^{3}) ((2 a^{2})^{2} - 2 a^{2} \cdot 3 b^{3} + (3 b^{3})^{2})

Simplify

(2 a^{2})^{2} - 2 a^{2} \cdot 3 b^{3} + (3 b^{3})^{2} : 4 a^{4} - 6 a^{2} b^{3} + 9 b^{6}

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

(4 a^{\frac{3}{2}}) (2 a^{\frac{1}{2}})

9 = t^{2} - 2 t + 1

5 - 3 (a + 6) = a - 1 + 8 a

\frac{32 a ^{5} b ^{- 3}}{8 a ^{- 2} b ^{6}}

6 x^{2} + 17 x = 3

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