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a)\(4x^4+y^4=\left(4x^4+y^4+4x^2y^2\right)-4x^2y^2\)
\(=\left(2x^2+y^2\right)^2-\left(2xy\right)^2\)
\(=\left(2x^2+y^2-2xy\right)\left(2x^2+y^2+2xy\right)\)
b)\(\left(x^2-3x-1\right)^2-12\left(x^2-3x-1\right)+27\)
Đặt x^2 - 3x - 1 = A
\(\Rightarrow A^2-12A+27=\left(A^2-12A+36\right)-9\)
\(=\left(A-6\right)^2-9=\left(A-6-3\right)\left(A-6+3\right)\)
\(=\left(A-9\right)\left(A-3\right)\)
Hay \(=\left(x^2-3x-1-9\right)\left(x^2-3x-1-3\right)\)
\(=\left(x^2-3x-10\right)\left(x^2-3x-4\right)\)
\(=\left(x-5\right)\left(x+2\right)\left(x-4\right)\left(x+1\right)\)
c)\(x^3-x^2-5x+125\)
\(=\left(x^3+5^3\right)-\left(x^2+5x\right)\)
\(=\left(x+5\right)\left(x^2-5x+25\right)-x\left(x+5\right)\)
\(=\left(x+5\right)\left(x^2-5x+25-x\right)\)
\(=\left(x+5\right)\left(x^2-6x+25\right)\)
d)\(xy\left(x+y\right)+yz\left(y+z\right)+zx\left(z+x\right)+2xyz\)
\(=\left(x+y\right)\left(y+z\right)\left(x+z\right)\)
Mình có việc bận nên chỉ đưa được kết quả ý d) thật lòng mong các bạn tự tham khảo và giải
a) \(4x^2-6x=2x\left(2x-3\right)\)
b) \(9x^4y^3+3x^2y^4=3x^2y^3\left(3x^2+y\right)\)
c) \(3\left(x-y\right)-5x\left(y-x\right)=3\left(x-y\right)+5x\left(x-y\right)\)
\(=\left(5x+3\right)\left(x-y\right)\)
d) \(x^3-2x^2+5x=x\left(x^2-2x+5\right)\)
e) \(5\left(x+3y\right)-15x\left(x+3y\right)=\left(5-15x\right)\left(x+3y\right)\)
\(=5\left(1-3x\right)\left(x+3y\right)\)
f) \(2x^2\left(x+1\right)-4\left(x+1\right)=\left(2x^2-4\right)\left(x+1\right)\)
\(=\left(\sqrt{2}x-2\right)\left(\sqrt{2}x+2\right)\left(x+1\right)\)
a/Dùng hằng đẳng thức A2-B2=(A+B)(A-B) phân tích được ngay
\(\left(x-y+4\right)^2-\left(2x+3y-1\right)^2\)
\(=\left(x-y+4+2x+3y-1\right)\left(x-y+4-2x-3y+1\right)\)
=\(\left(3x-2y+3\right)\left(4-x-4y\right)\)
b/Chắc chỉ phân tích hằng đẳng thức (A-B)2=A2-2ab+B2
\(49\left(y-4\right)^2-9y^2-3y-36=49y^2-392y+784-9y^2-3y-36\)
\(=40y^2-395y+748\)
Mình dùng biệt thức cho ra nghiệm vô tỉ, không biết cho phải tại mình tính sai hay đề thiếu nữa
c/Khai triển biểu thức ban đầu ta được
\(x\left(x-y\right)+y\left(y-x\right)=x^2-xy+y^2-xy=x^2-2xy+y^2=\left(x-y\right)^2\)
1 ) \(x^2+xy+x=x\left(x+1+y\right)\)
2 ) \(3x^2\left(x-1\right)+5x\left(1-x\right)=3x^2\left(x-1\right)-5x\left(x-1\right)=\left(3x^2-5x\right)\left(x-1\right)\)
3 ) \(2x\left(x+y\right)-3x-3y=2x\left(x+y\right)-3\left(x+y\right)=\left(2x-3\right)\left(x+y\right)\)
4 ) \(x\left(x-y\right)+y\left(y-x\right)=x\left(x-y\right)-y\left(x-y\right)=\left(x-y\right)\left(x-y\right)=\left(x-y\right)^2\)
5 ) \(4x^2-36=4\left(x^2-9\right)=4\left(x+3\right)\left(x-3\right)\)
4x2 - 36
= 4.x2 - 4.9
= 4(x2 - 9)
x2 + xy + x
= x.x + xy + x
= x(x + y + 1)
1) \(x^2+xy+x\)
\(=x\left(x+y+1\right)\)
2) \(3x^2\left(x-1\right)+5x\left(1-x\right)\)
\(=3x^2\left(x-1\right)-5x\left(x-1\right)\)
\(=\left(x-1\right)\left(3x^2-5x\right)\)
\(=\left(x-1\right)\times x\left(3x-5\right)\)
3) \(2x\left(x+y\right)-3x-3y\)
\(=2x\left(x+y\right)-3\left(x-y\right)\)
\(=2x\left(x+y\right)+3\left(x+y\right)\)
\(=\left(x+y\right)\left(2x+3\right)\)
1) \(x^2+xy+x=x\left(x+y+1\right)\)
2) \(3x^2\left(x-1\right)+5x\left(1-x\right)=3x^2\left(x-1\right)-5x\left(x-1\right)\)
\(\left(3x^2-5x\right)\left(x-1\right)=x\left(3x-5\right)\left(x-1\right)\)
3) \(2x\left(x+y\right)-3x-3y=2x\left(x+y\right)-\left(3x+3y\right)\)
\(2x\left(x+y\right)-3\left(x+y\right)=\left(2x-3\right)\left(x+y\right)\)
4) \(x\left(x-y\right)+y\left(y-x\right)=x\left(x-y\right)-y\left(x+y\right)\)
\(=\left(x-y\right)\left(x-y\right)=\left(x-y\right)^2\)
5) \(4x^2-36=\left(2x\right)^2-6^2\)
\(=\left(2x+6\right)\left(2x-6\right)\)
5) \(4x^2-36=\left(2x\right)^2-6^2\) \(=\left(2x+6\right)\left(2x-6\right)\)
4) \(x\left(x-y\right)+y\left(y-x\right)\)\(=x\left(x-y\right)-y\left(x-y\right)\) \(=\left(x-y\right)\left(x-y\right)=\left(x-y\right)^2\)
3) \(2x\left(x+y\right)-3x-3y\) \(=2x\left(x+y\right)-\left(3x+3y\right)\) \(=2x\left(x+y\right)-3\left(x+y\right)\)\(=\left(x+y\right)\left(2x-3\right)\)
2) \(3x^2\left(x-1\right)+5x\left(1-x\right)\)\(=3x^2\left(x-1\right)-5x\left(x-1\right)\) \(=\left(x-1\right)\left(3x^2-5x\right)\)
1) \(x^2+xy+x=x\left(x+y+1\right)\)
1) = x.(x+y) + x = x.(x+y+1)
2) =3x^2(x-1) - 5x(x-1)=(x-1)(3x^2 - 5x)
3) =2x(x+y) - 3.(x+y) = (x+y)(2x-3)
4) =x(x-y) - y(x-y) = (x-y)(x-y) = (x-y)2
5) = (2x)2 - 62 = (2x-6)(2x+6)
K mk nha