Phân tích đa thứ thành nhân tử
a) 4(x+y+z)^2-9(x-y-z)^2
b) 25(x-3y)^2-4(x+3y)^2
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BH
4 tháng 10 2016
a)\(a^4+a^3+a^3b+a^2b=\left(a^4+a^3b\right)+\left(a^3+a^2b\right)\)
\(=a^3\left(a+b\right)+a^2\left(a+b\right)\)
\(=\left(a^3+a^2\right)\left(a+b\right)\)
\(=a^2\left(a+1\right)\left(a+b\right)\)
b)\(\left(x-y+4\right)^2-\left(2x+3y-1\right)^2\)
\(=\left[\left(x-y+4\right)-\left(2x+3y-1\right)\right]\left[\left(x-y+4\right)+\left(2x+3y-1\right)\right]\)
\(=\left(x-y+4-2x-3y+1\right)\left(x-y+4+2x+3y-1\right)\)
\(=\left(-x-4y+5\right)\left(4x+2y+3\right)\)
c)\(x^2\left(y-z\right)+y^2\left(z-x\right)+z^2\left(x-y\right)\)
\(=x^2\left(y-z\right)+y^2\left(z-y+y-x\right)+z^2\left(x-y\right)\)
\(=x^2\left(y-z\right)-y^2\left(y-z\right)-y^2\left(x-y\right)+z^2\left(x-y\right)\)
\(=\left(y-z\right)\left(x^2-y^2\right)-\left(x-y\right)\left(y^2-z^2\right)\)
\(=\left(y-z\right)\left(x-y\right)\left(x+y\right)-\left(x-y\right)\left(y-z\right)\left(y+z\right)\)
\(=\left(y-z\right)\left(x-y\right)\left(x+y-y-z\right)\)
\(=\left(y-z\right)\left(x-y\right)\left(x-z\right)\)
12 tháng 10 2021
Bài 2:
a: \(3x^2-3xy=3x\left(x-y\right)\)
b: \(x^2-4y^2=\left(x-2y\right)\left(x+2y\right)\)
c: \(3x-3y+xy-y^2=\left(x-y\right)\left(3+y\right)\)
d: \(x^2-y^2+2y-1=\left(x-y+1\right)\left(x+y-1\right)\)
17 tháng 9 2018
\(a,=\left(4x^2\right)^2\left(x-y\right)-\left(x-y\right)\)
\(=\left[\left(4x^2\right)^2-1^2\right]\left(x-y\right)\)
\(=\left(4x^2+1\right)\left(4x^2-1\right)\left(x-y\right)\)
\(=\left(4x^2+1\right)\left(2x+1\right)\left(2x-1\right)\left(x-y\right)\)
a, \(4\left(x+y+z\right)^2-9\left(x-y-z\right)^2\)
\(=\left[2\left(x+y+z\right)\right]^2-\left[3\left(x-y-z\right)\right]^2\)
\(=\left[2x+2y+2z\right]^2-\left[3x-3y-3z\right]^2\)
\(=\left[\left(2x+2y+2z\right)-\left(3x-3y-3z\right)\right].\left[\left(2x+2y+2z\right)+\left(3x-3y-3z\right)\right]\)
\(=\left(-x+5y+5z\right)\left(5x-y-z\right)\)
b, \(25\left(x-3y\right)^2-4\left(x+3y\right)^2\)
\(=\left[5\left(x-3y\right)\right]^2-\left[2\left(x+3y\right)\right]^2\)
\(=\left[5x-15y\right]^2-\left[2x+6y\right]^2\)
\(=\left[5x-15y-2x-6y\right].\left[5x-15y+2x+6y\right]\)
\(=\left(3x-21y\right)\left(7x-9y\right)\)
\(=3\left(x-7y\right)\left(7x-9y\right)\)
Chúc bạn học tốt.
thks bn nha