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\(3a^2-6ab+3b^2-12c^2\)

\(=3\left(a^2-2ab+b^2-4c^2\right)\)

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

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

3a² - 6ab + 3b² - 12c² = 3.(a² - 2ab + b² - 4c²) = 3.[(a - b)² - 4c²] = 3.(a - b - 2c).(a - b + 2c)

a) 3a²-6ab+3b²-12c²

=3.(a²-2ab+b²-4c²)

=3.[(a-b)²-4c²]

=3.(a-b-2c)(a-b+2c)

\(3a^2-6ab-3b^2-12c^2=3\left(a^2-2ab+b^2\right)-12c^2=\left(\sqrt{3}\left(a-b\right)\right)^2-\left(\sqrt{12}c\right)^2=\left(\sqrt{3}a-\sqrt{3}b-\sqrt{12}c\right)\left(\sqrt{3}a-\sqrt{3}b+\sqrt{12}c\right)\)

Sửa đề :\(3a^2-6ab+3b^2-12c^2\)=\(3\left(a^2-2ab+b^2-4c^2\right)\)

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

3a² - 6ab + 3b² - 12c²

⁼ 3a² - 3a x 2b + 3b² - 3 x 4c²

= 3(a² -a x b +b² - 4c²)

phân tích thành nhân tử :
3a² - 6ab + 3b² - 12c²

=3(a\(^2\)-2ab+b\(^2\)-4c\(^2\))

=3[(a-b)\(^2\)-(2c)\(^2\)]

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

\(A=3a^2c^2+bd+3abc+acd=\left(3a^2c^2+3abc\right)+\left(bd+acd\right)=3ac\left(ac+b\right)+d\left(b+ac\right)\\ =\left(3ac+d\right)\left(ac+b\right)\)

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

\(C=8x^2+4xy-2ax-ay=\left(8x^2+4xy\right)-\left(2ax+ay\right)=4x\left(2x+y\right)-a\left(2x+y\right)\\ =\left(4x-a\right)\left(2x+y\right)\)

\(E=3a^2-6ab+3b^2-12c^2=3\left(a^2-2ab+b^2\right)-12c^2=3\left(a-b\right)^2-12c^2\\ =3\left[\left(a-b\right)^2-4c^2\right]=3\left(a-b-2c\right)\left(a-b+2c\right)\)

3a^2 -6ab +3ab^2 -12c^2

= 3(a^2 -2ab +b^2 -4c^2)

= 3[(a- b)^2 -4c^2]=3(a- b+ 4c)(a- b- 4c)

3a² - 6ab + 3b² - 12c²

= 3a² - 3.2ab + 3b² - 3.4c²

= 3 (a² - 2ab + b² - 4c²)

\(3a^2-6ab+3b^2-12c^2\)

\(=3a^2-3ab-3ab+3b^2-12c^2\)

\(=\left(3a^2-3ab\right)-\left(3ab-3b^2\right)-12c^2\)

\(=3a\left(a-b\right)-3b\left(a-b\right)-12c^2\)

\(=\left(3a-3b\right)\left(a-b\right)-12c^2\)

\(=3\left(a-b\right)^2-12c^2\)

3a² - 6ab + 3b² - 12c²

= 3(a² - 2ab + b² - 4c²)

= 3[(a - b)² - (2c)²]

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