Question

1. Rút gọn

a) (a+b+c)²-(a+b)²-c²

b) (a+b+c)²-(b+c)²-2a(b+c)

c) (3a+1)²-2(2a+5).(3a+1)+(2a+5)²

Answer 1

a)\(\left(a+b+c\right)^2-\left(a+b\right)^2-c^2\\ =\left(a+b\right)^2+2\left(a+b\right)c+c^2-\left(a+b\right)^2-c^2\\ =2\left(a+b\right)c\)

b)\(\left(a+b+c\right)^2-\left(b+c\right)^2-2a\left(b+c\right)\\ =a^2+2a\left(b+c\right)+\left(b+c\right)^2-\left(b+c\right)^2-2a\left(b+c\right)\\ =a^2\)

c)\(\left(3a+1\right)^2-2\left(2a+5\right)\left(3a+1\right)+\left(2a+5\right)^2\\ =\left(3a+1-2a-5\right)^2\\ =\left(a-4\right)^2\)