Question

•factorise the polynomial.
i need the help for this question​

Answer 1

Answer:

$(2)(a+b+c)(a^{2}+b^{2}+c^{2}-ab-bc-ca )$

Step-by-step explanation:

${(a+b)}^{3} +{(b+c)}^{3} +{(c+a)}^{3} -(3)(a+b)(b+c)(c+a)$

let a be (a+b)

let b be (b+c)

let c be (c+a)

Therefore, Using Identity- a³+b³+c³+3abc=(a+b+c)(a²+b²+c²-ab-bc-ca)-

$[(a+b)(b+c)(c+a)][{(a+b)}^{2} +(b+c)}^{2}+(c+a)}^{2}-(a+b)(b+c)-(b+c)(c+a)-(c+a)(a+b)]\\\\=>(a+b+b+c+c+a)[(a^{2}+2ab+b^{2} )+(b^{2}+2bc+c^{2} )+(c^{2}+2ac+a^{2} )-(ab+ac+b^{2} +bc)-(bc+ab+c^{2}+ac )-(ac+ab+a^{2}+ab )]\\\\=>(2a+2b+2c)(a^{2}+2ab+b^{2} +b^{2}+2bc+c^{2} +c^{2}+2ac+a^{2}-ab-ac-b^{2} -bc-bc-ab-c^{2}-ac -ac-bc-a^{2}-ab )\\\\=>(2a+2b+2c)(a^{2}+b^{2} +c^{2}-ab-bc-ca)\\\\=>(2)(a+b+c)(a^{2}+b^{2}+c^{2}-ab-bc-ca )$