a: \(\left(xy+ab\right)^2+\left(bx-ay\right)^2\)

\(=x^2y^2+a^2b^2+x^2b^2+a^2y^2\)

\(=x^2\left(b^2+y^2\right)+a^2\left(b^2+y^2\right)\)

\(=\left(b^2+y^2\right)\left(x^2+a^2\right)\)

Bài 4: 

Ta có: \(\left(x^3-x^2\right)-4x^2+8x-4=0\)

\(\Leftrightarrow x^2\left(x-1\right)-4\left(x-1\right)^2=0\)

\(\Leftrightarrow\left(x-1\right)\left(x-2\right)^2=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)

a: \(x^2-4xy+4y^2-2x+4y-35\)

\(=\left(x^2-4xy+4y^2\right)-\left(2x-4y\right)-35\)

\(=\left(x-2y\right)^2-2\left(x-2y\right)-35\)

\(=\left(x-2y\right)^2-7\left(x-2y\right)+5\left(x-2y\right)-35\)

\(=\left(x-2y\right)\left(x-2y-7\right)+5\left(x-2y-7\right)\)

\(=\left(x-2y-7\right)\left(x-2y+5\right)\)

c: \(\left(xy+ab\right)^2+\left(ay-bx\right)^2\)

\(=x^2y^2+a^2b^2+2xyab+a^2y^2-2aybx+b^2x^2\)

\(=x^2y^2+a^2y^2+a^2b^2+b^2x^2\)

\(=y^2\left(x^2+a^2\right)+b^2\left(a^2+x^2\right)\)

\(=\left(x^2+a^2\right)\left(y^2+b^2\right)\)

x²-xy+2x-2y
= (x²-xy)+(2x-2y)
= x(x-y)+2(x-y)
= (x-y)(x+2)

ax+ay-2x-2y
= (ax+ay)-(2x+2y)
= a(x+y)-2(x+y)
=(x+y)(a-2)

ax²-3axy+bx-3by
= (ax²+bx)-(3axy+3by)
= x(ax+b)-3y(ax+b)
= (ax+b)(x-3y)

2a²-5by-5a²y+2bx
= (2a²-5a²y)+(2bx-5by)
= a²(2-5y)+b(2x-5y)

x²-xy+2x-2y=(x²-xy)+(2x-2y)=x(x-y)+2(x-y)=(x-y)(x+2)

ax+ay-2x-2y=(ax+ay)-(2x+2y)=a(x+y)-2(x+y)=(x+y)(a-2)

ax²-3axy+bx-3by=(ax²+bx)-(3axy+3by)=x(ax+b)-3y(ax+b)=(ax+b)(x-3y)

d)\(x^2-ax-bx+ab=x\left(x-a\right)-b\left(x-a\right)\)

                                         \(=\left(x-b\right)\left(x-a\right)\)

e)\(x^2y+xy^2-x-y=xy\left(x+y\right)-\left(x+y\right)\) 

                                        \(=\left(xy-1\right)\left(x+y\right)\)

f)\(ax^2+ay-bx^2-by=a\left(x^2+y\right)-b\left(x^2+y\right)\)

                                            \(=\left(a-b\right)\left(x^2+y\right)\)

các bạn không trả lời cho bạn à

Bạn cx có làm đc bài đó đâu Despicable

a) x⁶ - x⁴ - 9x³ + 9x²

= x⁴.(x² - 1) - 9x²(x - 1)

= x⁴.(x - 1)(x + 1) - 9x².(x - 1)

= (x - 1).[x⁴.(x + 1) - 9x²]

= x².(x - 1).[x².(x + 1) - 9]

b) (xy + 4)² - 4(x + y)²

= (xy + 4)² - [2(x + y)]²

= [xy + 4 - 2(x + y)] . [xy + 4 + 2(x + y)]

c) (ab - xy)² - (bx - ay)²

= [(ab - xy) - (bx - ay)] . [(ab - xy) + (bx - ay)]

= [ab - xy - bx + ay] . [ab - xy + bx - ay]

= [a.(b + y) - x.(b + y)] . [b(a + x) - y(a + x)]

= (a - x)(b + y).(b - y)(a + x) 

\(a,=x^2-mx-nx+mn=x\left(x-m\right)-n\left(x-m\right)=\left(x-n\right)\left(x-m\right)\\ b,=a\left(x-y\right)-b\left(x-y\right)+\left(a-b\right)\\ =\left(x-y\right)\left(a-b\right)+\left(a-b\right)=\left(a-b\right)\left(x-y+1\right)\)

b: \(=a\left(x-y\right)-b\left(x-y\right)+a-b\)

\(=\left(x-y+1\right)\left(a-b\right)\)

a) \(x^2-\left(m+n\right)x+mn=\left(x^2-n\cdot x\right)-\left(m\cdot x-m\cdot n\right)=x\left(x-n\right)-m\left(x-n\right)=\left(x-m\right)\left(x-n\right)\)

b) \(ax+by+a-bx-ay-b\)

   \(=\left(ax-ay+a\right)-\left(bx-by+b\right)\)

   \(=a\left(x-y+1\right)-b\left(x-y+1\right)\)

   \(\left(a-b\right)\left(x-y+1\right)\)

Ta có :

(xy-ab)^2+(bx-ay)^2
=a^2y^2+b^2x^2+x^2y^2+a^2b^2
=a^2(y^2+b^2)+x^2(y^2+b^2) 
=(a^2+x^2)(y^2+b^2)

Ta có :

(xy-ab)^2+(bx-ay)^2

=a^2y^2+b^2x^2+x^2y^2+a^2b^2

=a^2(y^2+b^2)+x^2(y^2+b^2) 

=(a^2+x^2)(y^2+b^2)

d: \(=-\left(x+\sqrt{x}-12\right)=-\left(\sqrt{x}+4\right)\left(\sqrt{x}-3\right)\)