Question

Simplify (2a+3b+c)^2+(2a-3b-c)^2

Answer 1

8a^2+10b^2+2c^2+12bc

Answer 2

Answer:

= (2a+3b+c)² + (2a-3b-c)²

= 8a²+18b²+2c²+12bc

Step-by-step explanation:

(2a+3b+c)² + (2a-3b-c)²

(a+b+c)² = a²+b²+c²+2ab+2bc+2ca

(2a+3b+c)² = (2a)²+(3b)²+(c)²+2×(2a)(3b)+2×(3b)(c)+2×(c)(2a)

(2a+3b+c)² = 4a²+9b²+c²+12ab+6bc+4ca     

(2a-3b-c)² = (2a)²+(-3b)²+(-c)²+2×(2a)(-3b)+2×(-3b)(-c)+2×(-c)(2a)

(2a-3b-c)² = 4a²+9b²+c²-12ab+6bc-4ca   

                   

= (2a+3b+c)² + (2a-3b-c)²

= (4a²+9b²+c²+12ab+6bc+4ca)+(4a²+9b²+c²-12ab+6bc-4ca)

= 4a²+9b²+c²+12ab+6bc+4ca+4a²+9b²+c²-12ab+6bc-4ca

= 8a²+18b²+2c²+12bc