1、x^2y-6xy^2+9y^2 2、（y^2+4^2）-16y^2 3、(a-b)m^2+(b-a)n^2 4. X ^ 3-2x [1 / 2 x ^ 2-3) (1 / 6 x-1) - 1 / 4 x] 5、(a+1)^2-(1-a)(-a-1) 6、[(2xy+3)(2xy-3)+（xy+3^2）]÷xy

1、x^2y-6xy^2+9y^2 2、（y^2+4^2）-16y^2 3、(a-b)m^2+(b-a)n^2 4. X ^ 3-2x [1 / 2 x ^ 2-3) (1 / 6 x-1) - 1 / 4 x] 5、(a+1)^2-(1-a)(-a-1) 6、[(2xy+3)(2xy-3)+（xy+3^2）]÷xy

1、x^2y-6xy^2+9y^2
=y(x²-6xy+9y)
2、（y^2+4）^2-16y^2
=(y²+4-4y)(y+4+4y)
=(y-2)²(y+2)²
3、(a-b)m^2+(b-a)n^2
=(a-b)m²-(a-b)n²
=(a-b)(m²-n²)
=(a-b)(m+n)(m-n)
4. X ^ 3-2x [1 / 2 x ^ 2-3) (1 / 6 x-1) - 1 / 4 x]
I can't see clearly
5、(a+1)^2-(1-a)(-a-1)
=(a+1)²-(a-1)(a+1)
=(a+1)(a+1-a+1)
=2(a+1)
6、[(2xy+3)(2xy-3)+（xy+3^2）]÷xy
=(4x²y²-9+xy+9)÷xy
=(4x²y²+xy)÷xy
=4xy+1

Factorization: x2 + 6xy + 9y2-16a2 + 8a-1

x2+6xy+9y2-16a2+8a-1=（x+3y）2-（16a2-8a+1）=（x+3y）2-（4a-1）2=（x+3y-4a+1）（x+3y+4a-1）．

Factorization: x2 + 6xy + 9y2-16a2 + 8a-1

x2+6xy+9y2-16a2+8a-1=（x+3y）2-（16a2-8a+1）=（x+3y）2-（4a-1）2=（x+3y-4a+1）（x+3y+4a-1）．

Given the energy factorization (X-5) (x + a) of x2-3x + K, then k = ()

（x-5)*（x+a)=x^2+(a-5)x-5a
According to x2-3x + K: - 3 = a-5
The solution is a = 2
k= -5a= -10

Given a2-3ab + 2B2 = 0, find the value of 2a2-3ab + 52 / A2-B2 (specific process)

Because a & # 178; - 3AB + 2B & # 178; = 0
So: (2a-3ab + b-178;) / (a-178; - b-178;)
=(a²-3ab+2b²+a²-b²)/(a²-b²)
=（a²-b²)/(a²-b²)
＝1

It is known that BD is the middle line of triangle ABC, and the perimeter of triangle abd is 3cm longer than that of triangle BCD. How about the size relationship between sides AB and BC?
How did you get it?

BD is the middle line of triangle ABC
So ad = CD
The perimeter of the triangle abd is ab + BD + ad
The perimeter of triangle BCD is BC + BD + CD
The perimeter of the triangle abd is 3 cm longer than that of the triangle BCD
So AB + BD + ad-bc-bd-cd
=AB-BC=3cm
So AB is 3cm longer than BC

How many square meters is one foot, or how many feet is one square meter?

Feet is length, square meters is area, how can it be equal to? If you want to ask how many square feet one square meter equals, it's almost the same! I only know that one meter equals three feet!

The area of a trapezoid is 68.4 square decimeters, and the sum of its upper and lower bottoms is 36 decimeters. How high is the trapezoid?

H = 68.4 * 2 / 36 = 3.8 cm

As shown in the figure, make three equilateral triangles with three sides of triangle ABC as sides. 1) prove that the quadrilateral ADEF is a parallelogram;
2) When triangle ABC satisfies what condition, is quadrangle ADEF diamond? Rectangle?
3) Is there such a parallelogram ADEF?

(1) It is proved that: ∵ abd, △ BCE, △ ACF are equilateral triangles, ∵ AB = BD = ad, ∵ abd = ∠ EBC = ∠ BCE = ∠ ACF = 60 °, BC = be = CE, AC = AF = FC.