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câu 1.
P= 2(x+y)(x-y)+(x-y)^2+(x+y)^2-4y^2
P= (x+y+x-y)^2-(2y)^2
P=(2x-2y)(2x+2y)
P=4(x^2-y^2)
câu 2.
a, x^3-2x^2-4xy^2+x= x(x^2-2x+1)-4xy^2
=x(x-1)^2-4xy^2
=x(x-1-2y)(x-1+2y)
b, (x+1)(x+2)(x+3)(x+4)-24= (x^2+5x+4)(x^2+5x+6)-24
Đặt x^2+5x+4= a
Lúc đó: (x+1)(x+2)(x+3)(x+4)-24= a(a+2)-24
= a^2+2a-24
=a^2+2a+1-25
= (a+1)^2-5^2
= (a+1-5)(a+1+5)
= (a-4)(a+6)
mà ta đặt x^2+5x+4=a => (x+1)(x+2)(x+3)(x+4)-24= (x^2+5x+4-4)(x^2+5x+4+6)
= (x^2+5x)(x^2+5x+10)
câu3. (x+2)^2= 4-x^2
=> (x+2)^2-4+x^2=0
=>. (x+2)^2-(2-x)(2+x)=0
=> (x+2)(x+2-2+x)=0
=> (x+2)2x=0
=> x+2=0 hoặc 2x=0
=> x=-2 hoặc x=0
1)P=2(x^2-y^2)+x^2-2xy+y^2+x^2+2xy+y^2-4y^2=2x^2-2y^2+2x^2+2y^2-4y^2=4x^2-4y^2 . 3) <=> x^2+4x+4-4+x^2=0
<=> 2x^2+4x=0 <=>2x(x+2)=0 <=>2x=0 hay x+2=0 <=>x=0 hay x=-2
\(a,=\left(4x^2\right)^2\left(x-y\right)-\left(x-y\right)\)
\(=\left[\left(4x^2\right)^2-1^2\right]\left(x-y\right)\)
\(=\left(4x^2+1\right)\left(4x^2-1\right)\left(x-y\right)\)
\(=\left(4x^2+1\right)\left(2x+1\right)\left(2x-1\right)\left(x-y\right)\)
a) x2y3 - 1/2x4y8 = x2y3( 1 - 1/2x2y5 )
b) a2b4 + a3b - abc = ab( ab3 + a2 - c )
c) 7x( y - 4 )2 - ( y - 4 )3 = ( y - 4 )2( 7x - y + 4 )
d) -x2y2z - 6x3y - 8x4z2 - x2y2z2 = -x2( y2z + 6xy + 8x2z2 + y2z2 )
e) x3 - 4x2 + x = x( x2 - 4x + 1 )
\(1,\\ a,=4\left(x-2\right)^2+y\left(x-2\right)=\left(4x-8+y\right)\left(x-2\right)\\ b,=3a^2\left(x-y\right)+ab\left(x-y\right)=a\left(3a+b\right)\left(x-y\right)\\ 2,\\ a,=\left(x-y\right)\left[x\left(x-y\right)^2-y-y^2\right]\\ =\left(x-y\right)\left(x^3-2x^2y+xy^2-y-y^2\right)\\ b,=2ax^2\left(x+3\right)+6a\left(x+3\right)\\ =2a\left(x^2+3\right)\left(x+3\right)\\ 3,\\ a,=xy\left(x-y\right)-3\left(x-y\right)=\left(xy-3\right)\left(x-y\right)\\ b,Sửa:3ax^2+3bx^2+ax+bx+5a+5b\\ =3x^2\left(a+b\right)+x\left(a+b\right)+5\left(a+b\right)\\ =\left(3x^2+x+5\right)\left(a+b\right)\\ 4,\\ A=\left(b+3\right)\left(a-b\right)\\ A=\left(1997+3\right)\left(2003-1997\right)=2000\cdot6=12000\\ 5,\\ a,\Leftrightarrow\left(x-2017\right)\left(8x-2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=2017\\x=\dfrac{1}{4}\end{matrix}\right.\\ b,\Leftrightarrow\left(x-1\right)\left(x^2-16\right)=0\Leftrightarrow\left[{}\begin{matrix}x=1\\x=4\\x=-4\end{matrix}\right.\)