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\(=\left(x^2+y^2-5\right)^2-4\left(xy-2\right)^2=\left(x^2+y^2-5+2xy-4\right)\left(x^2+y^2-5-2xy+4\right)\)
\(=\left(\left(x+y\right)^2-9\right)\left(\left(x-y\right)^2-1\right)=\left(x+y-3\right)\left(x+y+3\right)\left(x-y+1\right)\left(x-y-1\right)\)
câu a nek
(4x^2 -7x-50)^2 -4x^2 (4x^2+14x+49/4)
= (4x^2 -7x-50)^2 -(2x)^2 (2x+7/2)^2
= (4x^2 -7x-50)^2 - (4x^2+7x)^2
= (4x^2 -7x-50 +4x^2+7x) (4x^2 -7x-50-4x^2-7x)
= (8x^2-50) (-14x-50)
=2(4x^2-25)* (-2)(7x+25)
=-4 (2x-5)(2x+5)(7x+25)
g ) \(4x^2\left(x-2y\right)-\left(4x+1\right)\left(2y-x\right)\)
\(=4x^2\left(x-2y\right)+\left(4x+1\right)\left(x-2y\right)\)
\(=\left(4x^2+4x+1\right)\left(x-2y\right)\)
\(=\left(2x+1\right)^2\left(x-2y\right)\)
h ) \(x^2-ax^2-y+ay+cx^2-cy\)
\(=x^2\left(1-a+c\right)-y\left(1-a+c\right)\)
\(=\left(x^2-y\right)\left(1-a+c\right)\)
d)\(\left(x^2+y^2-z^2\right)^2-4x^2y^2\)
\(=\left(x^2+y^2-z^2+2xy\right)\left(x^2+y^2-z^2-2xy\right)\)
\(=\left[\left(x^2+2xy+y^2\right)-z^2\right]\left[\left(x^2-2xy+y^2\right)-z^2\right]\)
\(=\left[\left(x+y\right)^2-z^2\right]\left[\left(x-y\right)^2-z^2\right]\)
\(=\left(x+y-z\right)\left(x+y+z\right)\left(x-y-z\right)\left(x-y+z\right)\)
e)Đặt \(x^2+3x=a\)
Có: \(\left(x^2+3x+1\right)\left(x^2+3x-3\right)-5\)
\(=\left(a+1\right)\left(a-3\right)-5\)
\(=a^2-3a+a-3-5\)
\(=a^2-2a-8\)
\(=a^2+2x-4x-8\)
\(=a\left(a+2\right)-4\left(a+2\right)\)
\(=\left(a+2\right)\left(a-4\right)\)
\(=\left(x^2+3x+2\right)\left(x^2+3x-4\right)\)
\(=\left(x^2+x+2x+2\right)\left(x^2-x+4x-4\right)\)
\(=\left[x\left(x+1\right)+2\left(x+1\right)\right]\left[x\left(x-1\right)+4\left(x-1\right)\right]\)
\(=\left(x+1\right)\left(x+2\right)\left(x-1\right)\left(x+4\right)\)
\(d,\left(x^2+y^2-z^2\right)^2-4x^2y^2\)
\(=\left(x^2+y^2-z^2\right)^2-\left(2xy\right)^2\)
\(=\left(x^2+y^2-z^2-2xy\right)\left(x^2+y^2-z^2+2xy\right)\)
\(=\left[\left(x^2-2xy+y^2\right)-z^2\right]\left[\left(x^2+2xy+y^2\right)-z^z\right]\)
\(=\left[\left(x-y\right)^2-z^2\right]\left[\left(x+y\right)^2-z^2\right]\)
\(=\left(x-y-z\right)\left(x-y+z\right)\left(x+y-z\right)\left(x+y+z\right)\)
\(e,\left(x^2+3x+1\right)\left(x^2+3x-3\right)-5\left(1\right)\)
\(\text{Đặt }x^2+3x+\frac{1-3}{2}=t\)
\(\text{hay }x^2+3x-2=t\left(2\right)\)
\(\left(1\right)\Leftrightarrow\left(t+3\right)\left(t-1\right)-5\)
\(\Rightarrow t^2-t+3t-3-5\)
\(=t^2+2t-8\)
\(=t^2-2t+4t-8\)
\(=t\left(t-2\right)+4\left(t-2\right)\)
\(=\left(t-2\right)\left(t+4\right)\left(3\right)\)
\(\text{Thay (2) vào (3),ta được:}\)
\(\left(x^2+3x-2-2\right)\left(x^2+3x-2+4\right)\)
\(=\left(x^2+3x-4\right)\left(x^2+3x+2\right)\)
\(=\left(x^2-x+4x-4\right)\left(x^2+x+2x+2\right)\)
\(=\left[x\left(x-1\right)+4\left(x-1\right)\right]\left[x\left(x+1\right)+2\left(x+1\right)\right]\)
\(=\left(x-1\right)\left(x+4\right)\left(x+1\right)\left(x+2\right)\)
\(\left(2x-y\right)\left(x-y\right)-\left(3y-4x\right)^2+\left(y-2x\right)\left(2y-3x\right)\)
=(2x-y)(x-y)-(2x-y)(2y-3x)-(4x-3y)2
=(2x-3y)(x-y-2y+3x)-(4x-3y)2
=(2x-3y)(4x-3y)-(4x-3y)2
=(4x-3y)(2x-3y-4x+3y)
=(4x-3y))(-2x)
a, \(=12x^5+9x^3y^2-6x^2y^3-20x^4y-15x^2y^3-10xy^4-24x^3y^2-18xy^4+12y^5\)
(tự rút gọn cái :P)
b, \(8x^3+4x^2y-2xy^2-y^3\)
\(=4x^2\left(2x+y\right)-y^2\left(2x+y\right)=\left(2x+y\right)^2\left(2x-y\right)\)
\(4x^2y^2-4x^2-4xy-y^2=4x^2y^2-\left(2x+y\right)^2\)
\(=\left(2x+y+2xy\right)\left(2xy-2x+y\right)\)
Mấy cái còn lại nhân tung ra là được mà :))))
a)
(x-y+5)2-2.(x-y+5)+1
=(x-y+5-1)2
=(x-y+4)2
b)
(x2+4y2-5)2-16.(x2.y2+2xy+1)
=(x2+4y2-5)2-[4.(xy+1)]2
=(x2+4y2-5-4xy-4)(x2+4y2-5+4xy+4)
=(x2+4y2-4xy-9)(x2+4y2+4xy-1)
=[(x-2y)2-9][(x+2y)2-1]
=(x-2y-3)(x-2y+3)(x+2y-1)(x+2y+1)
=(x2+x-3x-3)((x-2y+3)(x+2y-1)(x+1)2
=[x(x+1)-3(x+1)](x-2y+3)(x+2y-1)(x+1)2
=(x+1)(x-3)(x-2y+3)(x+2y-1)(x+1)2
(x2+y2−5)2−4x2y2−16xy−16
= (x2+y2−5)2− (4x2y2+16xy+16)
= (x2+y2−5)2− (22x2y2+16xy+42)
=(x2+y2−5)2− ((2xy)2+16xy+42)
=(x2+y2−5)2− (2xy+4)2
= (x2+y2−5+2xy+4)( x2+y2−5−2xy−4)
= (( x+y)2−1)((x−y)2−9)
= (x+y+1)(x+y−1)(x−y+3)(x−y−3)