Question

(a-b-c)(a²+b²+c²-ab+bc-ca) find the product without actual multiplication. ​

Answer 1

Answer:

(a-b-c)(a²+b²+c²-ab+bc-ca)

$= a^3 - b^3 - c^3+ ab^2 + ab^2+ ac^2+ ac^2 -a^2b + abc+ abc + abc- a^2c -ba^2 - bc^2 -bc^2 - cb^2 - cb^2$

Step-by-step explanation:

(a-b-c)(a²+b²+c²-ab+bc-ca)

= a (a²+b²+c²-ab+bc-ca) - b (a²+b²+c²-ab+bc-ca) - c (a²+b²+c²-ab+bc-ca)

= a(a²) + a(b²) +a(c²) - a(ab) + a(bc)-a (ca)-b(a²) -b(b²) -b(c²) +b(ab) -b(bc)+b (ca) -c(b²) -c(c²) +c(ab) -c(bc)+c (ca)

$= a^3 + ab^2 + ac^2 -a^2b + abc - a^2c -ba^2 - b^3 - bc^2 + ab^2 - cb^2 + abc - cb^2 - c^3 + abc -bc^2 + ac^2$

Rearrange similar terms

$= a^3 - b^3 - c^3+ ab^2 + ab^2+ ac^2+ ac^2 -a^2b + abc+ abc + abc- a^2c -ba^2 - bc^2 -bc^2 - cb^2 - cb^2$