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\(1,\\ a,=4\left(x-2\right)^2+y\left(x-2\right)=\left(4x-8+y\right)\left(x-2\right)\\ b,=3a^2\left(x-y\right)+ab\left(x-y\right)=a\left(3a+b\right)\left(x-y\right)\\ 2,\\ a,=\left(x-y\right)\left[x\left(x-y\right)^2-y-y^2\right]\\ =\left(x-y\right)\left(x^3-2x^2y+xy^2-y-y^2\right)\\ b,=2ax^2\left(x+3\right)+6a\left(x+3\right)\\ =2a\left(x^2+3\right)\left(x+3\right)\\ 3,\\ a,=xy\left(x-y\right)-3\left(x-y\right)=\left(xy-3\right)\left(x-y\right)\\ b,Sửa:3ax^2+3bx^2+ax+bx+5a+5b\\ =3x^2\left(a+b\right)+x\left(a+b\right)+5\left(a+b\right)\\ =\left(3x^2+x+5\right)\left(a+b\right)\\ 4,\\ A=\left(b+3\right)\left(a-b\right)\\ A=\left(1997+3\right)\left(2003-1997\right)=2000\cdot6=12000\\ 5,\\ a,\Leftrightarrow\left(x-2017\right)\left(8x-2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=2017\\x=\dfrac{1}{4}\end{matrix}\right.\\ b,\Leftrightarrow\left(x-1\right)\left(x^2-16\right)=0\Leftrightarrow\left[{}\begin{matrix}x=1\\x=4\\x=-4\end{matrix}\right.\)
Bạn nên viết lại đa thức bằng công thức toán (biểu tượng $\sum$ góc trái khung soạn thảo) để được hỗ trợ tốt hơn.
1: \(x-9=\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)\)
2: \(x-16=\left(\sqrt{x}-4\right)\left(\sqrt{x}+4\right)\)
3: \(9x-1=\left(3\sqrt{x}-1\right)\left(3\sqrt{x}+1\right)\)
4: \(x\sqrt{x}+1=\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)\)
\(1,x-9=\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)\\ 2,x-16=\left(\sqrt{x}-4\right)\left(\sqrt{x}+4\right)\\ 3,9x-1=\left(3\sqrt{x}-1\right)\left(3\sqrt{x}+1\right)\\ 4,x\sqrt{x}+1=\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)\)
Ta có \(f\left(x\right)=\left(x+1\right)\left(x-3\right)\left(x+5\right)\left(x+9\right)+256\)
\(f\left(x\right)=\left(x+1\right)\left(x+5\right)\left(x-3\right)\left(x+9\right)+256\)
\(f\left(x\right)=\left(x^2+6x+5\right)\left(x^2+6x-27\right)+256\)
\(f\left(x\right)=\left[\left(x^2+6x-11\right)^2-256\right]+256\)
\(f\left(x\right)=\left(x^2+6x-11\right)^2\)
\(1,=x\left(x^2-2x+1-y^2\right)=x\left[\left(x-1\right)^2-y^2\right]=x\left(x-y-1\right)\left(x+y-1\right)\\ 2,=\left(x+y\right)^3\\ 3,=\left(2y-z\right)\left(4x+7y\right)\\ 4,=\left(x+2\right)^2\\ 5,Sửa:x\left(x-2\right)-x+2=0\\ \Leftrightarrow\left(x-2\right)\left(x-1\right)=0\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)
3 . (x+3) - x2+9
= 3.(x+3)-(x2-9)
=3.(x+3)-[(x-3).(x+3)]
=(x+3).[3-(x-3)]
=(x+3).(3-x+3)
=(x+3).(9-x)
x9+x3+x2+x1
= (x9-x6)+(x6-x3)+x2+x+1
= x6(x3-1)+x3(x3-1)+x2+x+1
= x6(x-1)(x2+x+1)+x3(x-1)(x2+x+1)+(x2+x+1)
= (x2+x+1)(x7-x6+x4-x3+1)