If a - 2b + 3c = 0; State the Value of A3 - 8b3 + 27c3. - Mathematics

If a - 2b + 3c = 0; state the value of a³- 8b³ + 27c³.

Sum

a³- 8b³ + 27c³ = a³ + (-2b)³ + (3c)³Since a - 2b + 3c = 0, we have
a³- 8b³ + 27c³= a³ + (-2b)³ + (3c)³= 3(a)( -2b)(3c)
= -18abc

shaalaa.com

Special Product

Is there an error in this question or solution?

Chapter 4: Expansions (Including Substitution) - Exercise 4 (E) [Page 66]

Chapter 4 Expansions (Including Substitution)
Exercise 4 (E) | Q 6 | Page 66

Simplify : ( x - 6 )( x - 4 )( x + 2 )

Simplify : ( x - 6 )( x - 4 )( x - 2 )

Simplify using following identity : `( a +- b )(a^2 +- ab + b^2) = a^3 +- b^3`
`( 3x - 5/x )( 9x^2 + 15 + 25/x^2)`

Simplify using following identity : `( a +- b )(a^2 +- ab + b^2) = a^3 +- b^3`
`(a/3 - 3b)(a^2/9 + ab + 9b^2)`

Find : (a - b)(a - b)(a - b)

If x + 5y = 10; find the value of x³ + 125y³ + 150xy - 1000.

Using suitable identity, evaluate (104)³

Simplify :
`[(x^2 - y^2)^3 + (y^2 - z^2)^3 + (z^2 - x^2)^3]/[(x - y)^3 + (y - z)^3 + (z - x)^3]`

Evaluate :
`[0.8 xx 0.8 xx 0.8 + 0.5 xx 0.5 xx 0.5]/[0.8 xx 0.8 - 0.8 xx 0.5 + 0.5 xx .5]`

Evaluate :
`[1.2 xx 1.2 + 1.2 xx 0.3 + 0.3 xx 0.3 ]/[ 1.2 xx 1.2 xx 1.2 - 0.3 xx 0.3 xx 0.3]`