Question

Factorise a. 2xCube -5 xSquare - 23 x -10
b. 27mCube- 343nCube

Answer 1

Question:-

Factorise $:\rightarrow$

(a) ${2x}^{3}-{5x}^{2}-23x-10$

(b)${27m}^{3}-{343n}^{3}$

$\quad$

Solution:-

(a) ${2x}^{3}-{5x}^{2}-23x-10$

( By Grouping )

${2x}^{3}- {5x}^{2} - 23x - 10$

$= {2x}^{3} + {5x}^{2} + 2x - {10x }^{2} - 25x - 10$

$= x( {2x}^{2} + 5x + 2) - 5( {2x}^{2} + 5x + 2)$

$= (x - 5)( {2x}^{2} + 5x + 2)$

$= (x - 5)( {2x}^{2} + 4x + x + 2)$

$=(x - 5)(2 ({x}^{2} + 2x) + x + 2)$

$= (x - 5)(2x(x + 2) + x + 2)$

$= (x - 5)(x + 2)(2x + 1)$

$\:$

(b) ${27m}^{3}-{343n}^{3}$

Using Identity:-

${a}^{3} - {b}^{3} = (a - b( {a}^{2} + ab + {b}^{2} )$

$27 {m}^{3} - 343 {n}^{3} = (2 {m}^{3} - 7 {n}^{3} )$

$=(2m-7n)(2{m}^{2})+2m\times7n+({7n}^{2})$

$= ( 2m - 7n)(4 {m}^{2} + 14mn + 49 {n}^{2} )$