Question

phân tích đa thức thành nhân tử (a+b+c)^2+(a-b+c)^2-4b^2

Answer 1

\(\left(a+b+c\right)^2+\left(a-b+c\right)^2-4b^2\)

\(=2a^2+2b^2+2c^2+2ab+2ac+2bc-2ab-2bc+2ac-4b^2\)

\(=2a^2-2b^2+2c^2+4ac\)

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

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

Answer 2

\(\left(a+b+c\right)^2-\left(a-b+c\right)^2-4b^2\)

\(=a^2+b^2+c^2+2ab+2bc+2ca+a^2+b^2+c^2-2ab-2bc+2ca-4b^2\)

\(=2a^2-2b^2+2c^2+4ca\)

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

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

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

Answer 3

(a+b+c)^2+(a-b+c)^2-4b^2 =(a+b+c)^2+(a-b+c-2b)×(a-b+c+2b) =(a+b+c)^2+(a+c-3b)×(a+b+c) =(a+b+c)^2×(a+b+c+a-3b+c) =(a+b+c)^2×(2a-2b+2c) =2(a+b+c)×(a-b+c) Câu trả lời đúng đây ạ😄