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\(1,\\ a,=4\left(x-2\right)^2+y\left(x-2\right)=\left(4x-8+y\right)\left(x-2\right)\\ b,=3a^2\left(x-y\right)+ab\left(x-y\right)=a\left(3a+b\right)\left(x-y\right)\\ 2,\\ a,=\left(x-y\right)\left[x\left(x-y\right)^2-y-y^2\right]\\ =\left(x-y\right)\left(x^3-2x^2y+xy^2-y-y^2\right)\\ b,=2ax^2\left(x+3\right)+6a\left(x+3\right)\\ =2a\left(x^2+3\right)\left(x+3\right)\\ 3,\\ a,=xy\left(x-y\right)-3\left(x-y\right)=\left(xy-3\right)\left(x-y\right)\\ b,Sửa:3ax^2+3bx^2+ax+bx+5a+5b\\ =3x^2\left(a+b\right)+x\left(a+b\right)+5\left(a+b\right)\\ =\left(3x^2+x+5\right)\left(a+b\right)\\ 4,\\ A=\left(b+3\right)\left(a-b\right)\\ A=\left(1997+3\right)\left(2003-1997\right)=2000\cdot6=12000\\ 5,\\ a,\Leftrightarrow\left(x-2017\right)\left(8x-2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=2017\\x=\dfrac{1}{4}\end{matrix}\right.\\ b,\Leftrightarrow\left(x-1\right)\left(x^2-16\right)=0\Leftrightarrow\left[{}\begin{matrix}x=1\\x=4\\x=-4\end{matrix}\right.\)
a) Ta có: \(a^2-b^2-5a+5b\)
\(=\left(a-b\right)\left(a+b\right)-5\left(a-b\right)\)
\(=\left(a-b\right)\left(a+b-5\right)\)
b) Ta có: \(a^2-b^2-3ab^2-3a^2b\)
\(=\left(a-b\right)\left(a+b\right)-3ab\left(a+b\right)\)
\(=\left(a+b\right)\left(a-b-3ab\right)\)
a) 25 - x2 + 4xy - 4y2 = 25 - (x2 - 4xy + 4y2) = 52 - (x - 2y)2 = (5 + x - 2y)(5 - x +2y) = (x - 2y + 5)(2y - x + 5)
b) 3a2c2 + bd + 3abc + acd = (3a2c2 + 3abc) + (bd + acd) = 3ac(ac + b) + d (ac + b) = (ac + b)(3ac + d)
c) x3 - 2x2 - x + 2 = x2(x - 2) - (x - 2) = (x - 2)(x2 - 1) = (x - 2)(x - 1)(x + 1)
d) a4 + 5a3 + 15a - 9 = (a4 + 3a2) + (5a3 + 15a) - (3a2 + 9) = a2(a2 + 3) + 5a(a2 + 3) - 3(a2 + 3) = (a2 + 3)(a2 + 5a - 3)
b)\(2a^2-3+5a\)
\(=\left(2a^2+6a\right)-\left(a+3\right)\)
\(=\left(a+3\right)\left(2a-1\right)\)
d)\(2a^2-5-3a\)
\(=\left(2a^2+2a\right)-\left(5a+5\right)\)
\(=\left(a+1\right)\left(2a-5\right)\)
a) \(a^2-3-2a\)
\(=a^2-2a+1-4\)
\(=\left(a^2-2a+1\right)-2^2\)
\(=\left(a-1\right)^2-2^2\)
\(=\left(a-1-2\right)\left(a-1+2\right)\)
\(=\left(a-3\right)\left(a+1\right)\)
c) \(4a+a^2+3\)
\(=a^2+4a+4-1\)
\(=\left(a^2+4a+4\right)-1^2\)
\(=\left(a+2\right)^2-1^2\)
\(=\left(a+2-1\right)\left(a+2+1\right)\)
\(=\left(a+1\right)\left(a+3\right)\)
\(a^3-b^3+3a^2+3ab+b^2\)
\(=\left(a-b\right)\left(a^2+ab+b^2\right)+3\left(a^2+ab+b^2\right)\)
\(=\left(a-b+3\right)\left(a^2+ab+b^2\right)\)