a: =x^2+2xy+y^2-4x^2y^2

=(x+y)^2-(2xy)^2

=(x+y+2xy)(x+y-2xy)

b: =49-(a^2-2ab+b^2)

=49-(a-b)^2

=(7-a+b)(7+a-b)

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

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

d: 

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

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

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

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

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

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

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

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

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

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

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

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

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

Mn vào tcn của con này, https://olm.vn/thanhvien/kimmai123az, PTD/KM ?, nó chuyên đi copy bài của ng khác và câu hỏi tương tự

a) (a+b+c)^2 + (a+b-c)^2 - 4c^2

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

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

\(=\left(a+b+c\right)^2+\left(a+b+c\right)\left(a+b-3c\right)\)

\(=\left(a+b+c\right)\left(a+b+c+a+b-3c\right)\)

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

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

b) 4a^2b^2 - (a^2+b^2-c^2)^2

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

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

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

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

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

\(=ab^3-ac^3+bc^3-a^3b+a^3c-b^3c\)

\(=a^3\left(c-b\right)+bc\left(c-b\right)\left(c+b\right)-a\left(c-b\right)\left(c^2+bc+b^2\right)\)

\(=a^3\left(c-b\right)+\left(c-b\right)\left(bc^2+b^2c\right)-\left(c-b\right)\left(ac^2+abc+ab^2\right)\)

\(=\left(c-b\right)\left(a^3+bc^2+b^2c-ac^2-abc-ab^2\right)\)

a) (a+b+c)^2 + (a+b-c)^2 - 4c^2

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

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

\(=\left(a+b+c\right)^2+\left(a+b+c\right)\left(a+b-3c\right)\)

\(=\left(a+b+c\right)\left(a+b+c+a+b-3c\right)\)

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

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

b) 4a^2b^2 - (a^2+b^2-c^2)^2

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

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

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

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

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

\(=ab^3-ac^3+bc^3-a^3b+a^3c-b^3c\)

\(=a^3\left(c-b\right)+bc\left(c-b\right)\left(c+b\right)-a\left(c-b\right)\left(c^2+bc+b^2\right)\)

\(=a^3\left(c-b\right)+\left(c-b\right)\left(bc^2+b^2c\right)-\left(c-b\right)\left(ac^2+abc+ab^2\right)\)

\(=\left(c-b\right)\left(a^3+bc^2+b^2c-ac^2-abc-ab^2\right)\)

ta có: \(\left(a+b+c\right)^2+\left(a+b-c\right)^2-4c^2=\left(a+b+c\right)^2+\left(a+b-c-2c\right)\left(a+b-c+2c\right).\)

                                                                                         \(=\left(a+b+c\right)^2+\left(a+b-3c\right)\left(a+b+c\right)\)

                                                                                          \(=\left(a+b+c\right)\left(a+b+c+a+b-3c\right)\)

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

(a+b+c)^2+(a+b-c)^2-4c^2

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

=a^2+b^2+c^2+2ab+2bc+2ac+a^2-2ab+b^2-2ac+c^2-abc-4c^2

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

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

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

=2*(a^2+b^2)+2c^2*(1-2)

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

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

\(=\left(a+b+c\right)^2+\left(a+b+c\right)\left(a+b-3c\right)\)

\(=\left(a+b+c\right)\left(a+b+c+a+b-3c\right)\)

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

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

a) = (x^2-2xy+y^2)-(4m^2-4mn+n^2)

=(x+y)^2-(2-n)^2

=(x+y-2+n)(x+y+2-n)

B) c/m tương tự nhé!

a)x²-2xy+y²-4m²+4mn-n²=(x²-2xy+y²)-((2m)²-4mn+n²)=(x-y)²-(2m-n)²=(x-y+2m-n)(x-y-2m+n)

b)(a+b+c)²+(a+b+c)²-4c²=(a+b+c)+(a+b+c)²-(2c)²=(a+b+c)²+(a+b+c+2c)(a+b+c-2c)=(a+b+c)²+(a+b+3c)(a+b-c)=(a+b-c)(a+b-c+a+b+3c)=(a+b-c)(2a+2b+2c)=2(a+b-c)(a+b+c)

mày vào tcn của tao, xong vô thống kê hỏi đáp của tao đi, rồi bấm vào 1 câu trả lời, mày là chó, chuyên đi copy bài ng khác và câu hỏi tunogw tự

a) x² - 2xy + y² - 4m² + 4mn - n² = (x - y)² - [(2m)² -  2.2m.n + n²] = (x - y)² - (2m - n)²

= [(x - y) - (2m - n)][(x - y) + (2m - n)] = (x - y - 2m + n)(x - y + 2m - n)

b) x² - 4x²y² + y² + 2xy = x² + 2xy + y² - 4x²y² = (x + y)² - (2xy)² = (x + y - 2xy)(x + y + 2xy)

c) x⁶ - y⁶ = (x³)² - (y³)² = (x³ - y³)(x³ + y³) = (x - y)(x² + xy + y²)(x + y)(x² - xy - y²)

d) 25 - a² + 2ab - b² = 25 - (a² - 2ab + b²) = 5² - (a - b)² = (5 - a + b)(5 + a - b)

xin lỗi các bạn, đề mink có vấn đề: ý c phải là: x^6 - y^6

\(x^6-y^6=\left(x^3\right)^2-\left(y^3\right)^2=\left(x^3+y^3\right)\left(x^3-y^3\right)=\)\(\left(x+y\right)\left(x^2-xy+y^2\right)\left(x-y\right)\left(x^2+xy+y^2\right)\)