Advertisements
Advertisements
Question
Factorise:
`2sqrt(2)a^3 + 8b^3 - 27c^3 + 18sqrt(2)abc`
Advertisements
Solution
`2sqrt(2)a^3 + 8b^3 - 27c^3 + 18sqrt(2)abc`
= `(sqrt(2)a)^3 + (2b)^3 + (-3c)^3 - 3(sqrt(2)a)(2b)(-3c)`
= `(sqrt(2)a + 2b - 3c)[(sqrt(2)a)^2 + (2b)^2 + (-3c)^2 - (sqrt(2)a)(2b) - (2b)(-3c) - (-3c)(sqrt(2)a)]` ...[Using identity, a3 + b3 + c3 – 3abc = (a + b + c)(a2 + b2 + c2 – ab – bc – ca)]
= `(sqrt(2)a + 2b - 3c)[2a^2 + 4b^2 + 9c^2 - 2sqrt(2)ab + 6bc + 3sqrt(2)ac]`
APPEARS IN
RELATED QUESTIONS
Find the value of k, if x – 1 is a factor of p(x) in the following case:
p(x) = `2x^2+kx+sqrt2`
Factorise:
3x2 – x – 4
Factorise:
x3 – 3x2 – 9x – 5
Factorize the following polynomial.
(y + 2) (y – 3) (y + 8) (y + 3) + 56
One of the factors of (25x2 – 1) + (1 + 5x)2 is ______.
Show that 2x – 3 is a factor of x + 2x3 – 9x2 + 12.
Factorise:
x2 + 9x + 18
Factorise:
2x2 – 7x – 15
Factorise the following:
`8p^3 + 12/5 p^2 + 6/25 p + 1/125`
Factorise:
1 + 64x3
