Question

simplify: (2a + 3b -c)² + (2a -3b +c)²​

Answer 1

(a+b+c)² = a²+b²+c²+2ab+2bc+2ca

= 4a²+9b²+c²+12ab+6bc+2ac

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Answer 2

Answer:

= (2a + 3b -c)² + (2a -3b +c)²

= 8a²+18b²+2c²-12bc

Step-by-step explanation:

(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×(2a)(−c)

(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