Calculate the square of (- x + 2Y) with the complete square formula

Calculate the square of (- x + 2Y) with the complete square formula

(-x + 2y)^2
= (-x)^2 + 2 × （-x ) × (2y) + (2y)^2
= x^2 + 4xy + 4y^2

Can the square of trinomial formula be expanded by the complete square formula? Try to calculate the square of (x-2y + 1 / 3)

(x-2y+1/3)^2
=[(x-2y)+1/3]^2
=(x-2y)^2+2*1/3*(x-2y)+(1/3)^2
=x^2-4xy+4y^2+2x/3-4y/3+1/9

Complete square formula (- x + 2Y) ^ 2

=(-x)^2+2(-x)(2y)+(2y)^2
=x^2-4xy+4y^2

Calculation of complete square formula and square difference formula: (2x-3y) 2; (- X-Y) 2 5

（2x-3y）²
=4x²-12xy+9y²
（-x-y）²
=x²+2xy+y²
If there is anything you don't understand, you can ask,

Calculation: (2x? 2 + 3Y) (3y-2x? 2) [square difference formula]

=(3y+2x²)(3y-2x²)
=(3y)²-（2x²)²
=The fourth power of 9y? - 4x

Calculation of (3 / 4x-2 / 3Y) 2 by using the complete square formula

﹙3/4x－2/3y﹚²=(9/16)x²+(4/9)y²-xy

Given that x? 2 + 4Y? - 2x = 4Y-2, the value of (2x-3y) 2 - (3y-x) 2 is obtained by using the complete square formula,

x²+4y²-2x=4y-2
x²+4y²-2x-4y+2=0
(x-1)^2+(2y-1)^2=0
X=1
y=1/2
（2x-3y）²-(3y-x)²
=(2x-3y-3y+x)(2x-3y+3y-x)
=(3x-6y)x
=3-3
=0

Calculate (2x-3y) 2 - (2x + 3Y) 2

The original formula is equal to 4x? + 9y? - 12xy - (4x? + 9y? + 12xy)
=4x²+9y²-12xy-4x²-9y²-12xy
=-24xy

Solve the following equation: (1) 2x2-5x + 1 = 0 (matching method) （2）16（x+5）2-8（x+5）=0

(1) Divide the two sides by two,
x2-5
2x+1
2=0，
⇒x2-5
2x+（5
4）2-（5
4）2+1
2=0，
∴（x-5
4）2=25−8
42，
X 1 = 5+
Seventeen
4，x2=5−
Seventeen
4．
（2）（x+5）（16x+16×5-8）=0，
X + 5 = 0 or 16x + 80-8 = 0,
The results show that X1 = - 5, X2 = - 4.5

2X ^ 2-5x + 8 / (2x ^ 2-5x + 1) - 5 = 0, find the value of 2x ^ 2-5x-1

Let a = 2x ^ 2-5x + 1, then
A-1+8/A-5=0
A+8/A-6=0
A^2-6A+8=0
(A-2)(A-4)=0
A = 2, or a = 4
Because a = 2x ^ 2-5x + 1 = 2 (X-5 / 4) ^ 2 - (17 / 8)
So a ≥ - 17 / 8
A = 2, or a = 4