What is factor (2+h)^{-3}+2^{-3} ?

The solution to factor (2+h)^{-3}+2^{-3} is ((h+4)(h^2+2h+4))/(8(h+2)^3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

factor (2+h)^{-3}+2^{-3}

factor

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

\frac{( h + 4 ) ( h ^{2} + 2 h + 4 )}{8 ( h + 2 ) ^{3}}

Solution steps

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

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

(2 + h)^{- 3} = \frac{1}{( 2 + h ) ^{3}}

= \frac{1}{( h + 2 ) ^{3}} + 2^{- 3}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

2^{- 3} = \frac{1}{2 ^{3}}

= \frac{1}{( h + 2 ) ^{3}} + \frac{1}{2 ^{3}}

2^{3} = 8

= \frac{1}{( 2 + h ) ^{3}} + \frac{1}{8}

Least Common Multiplier of

(2 + h)^{3}, 8 : 8 (h + 2)^{3}

Adjust Fractions based on the LCM

= \frac{8}{8 ( h + 2 ) ^{3}} + \frac{( h + 2 ) ^{3}}{8 ( h + 2 ) ^{3}}

Since the denominators are equal, combine the fractions:

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

= \frac{8 + ( h + 2 ) ^{3}}{8 ( h + 2 ) ^{3}}

Expand

8 + (h + 2)^{3} : h^{3} + 6 h^{2} + 12 h + 16

= \frac{h ^{3} + 6 h ^{2} + 12 h + 16}{8 ( h + 2 ) ^{3}}

Factor

h^{3} + 6 h^{2} + 12 h + 16 : (h + 4) (h^{2} + 2 h + 4)

= \frac{( h + 4 ) ( h ^{2} + 2 h + 4 )}{8 ( h + 2 ) ^{3}}

2 b x^{b - 3} + 6 x^{2}

- 29 + x^{2} + 4

838 \cdot 2.1

x^{34} - 2 x^{9}

4 e^{2} + 12 e

What is factor (2+h)^{-3}+2^{-3} ?
The solution to factor (2+h)^{-3}+2^{-3} is ((h+4)(h^2+2h+4))/(8(h+2)^3)