Question

Rút gọn

(a+b+c+d)^2+(a+b-c-d)^2+(a+c-b-d)^2+(a+d-b-c)^2

Answer 1

=[(a+b)+(c+d)]^2+[(a+b)-(c+d)]^2+[(a+c)-(b+d)]^2+[(a-c)-(b-d)]^2

=[(a+b)^2+2(a+b)(c+d)+(c+d)^2+(a+b)^2-2(a+b)(c+d)+(c+d)^2]+[(a+c)^2-2(a+c)(b+d)+(b+d)^2+(a-c)^2-2(a-c)(b-d)+(b-d)^2]

=[2(a+b)^2+2(c+d)^2]+[2a^2+2c^2-4ab+2b^2+2d^2]

={2[(a+b)^2+(c+d)^2]}+[(2a^2-4ab+2b^2)+(2c^2+2d^2)]

={2[(a+b)^2+(c+d)^2]}+[2(a-b)^2+2(c^2+d^2)]

={2[(a+b)^2+(c+d)^2]}+{2[(a-b)^2+(c^2+d^2)]}

=2a^2-4ab+2b^2+2c^2+2d^2+2a^2+4ab+2b^2+2c^2+2d^2

=4a^2+4b^2+4c^2+4d^2

=4(a^2+b^2+c^2+d^2)

nếu sai góp ý cho mk nha