The question of the perfect square formula, what is the problem of the calculation of the perfect sq

1.(_x_-1)^2=(__x^2_)-x/2+(_1_)2.If x+y=10, xy=24, find x 2-xy+y 2x+y) 2-3xy=28

3.If x+y=10 and xy=24, find the value of x2-xy+y2 as above. 4.It is known that x+y=a, xy=b, and the algebraic expressions containing a and b are used to express x2+y2 and (x-y)2, respectively

x^2+y^2=a^2-2b (x-y)^2=a^2-4b5.Knowing that a2+b 2+4a-6b+13=0, find the value of a,b.

a=-2 b=3

1.(_x/4__-1)^2=(__x^2/16_)-x/2+(_1_)

2.If x+y=10 and xy=24, find x2-xy+y2

3.If x+y=10 and xy=24, find the value of x2-xy+y2.

x^2-xy+y^2=(x+y)^2-3xy=100-72=28

4.It is known that x+y=a, xy=b, and the algebraic expressions containing a and b are used to express x2+y2 and (x-y)2, respectively

x^2+y^2=a^2-2b, (x-y)^2=a^2-2b-2b=a^2-4b

5.Knowing that a2+b 2+4a-6b+13=0, find the value of a,b.

a^2+b^2+4a-6b+13=(a+2)^2+(b-3)^2=0, a=-2,b=3.

The perfect square formula is calculated as follows:1、(x²+1)²-4x²。

2、(2x-y)²-2(2x-y)+1。

3、(x+y)²-2(x²-y²)+x-y)²4、（a+1）(a+5)+4。

5、（m²+n²）²4m²n²。

6、x²+2x+1-y²。

7、-4x^2+12xy-9y^2。

2a-b)^2-6(2a-b)+1。

9、-2m^3+24m^2-72m。

10、-x^4+2x^2y^2-y^4。

Definition. The sum of two numbers is equal to 2 times their sum of squares plus their product.

a+b）²=a²﹢2ab+b²

The square of the difference between the two numbers is equal to 2 times the sum of their squares minus the product of their tufts.

a－b﹚²=a²﹣2ab+b²

This formula is an important knowledge base for algebraic operations and deformation, and it is a commonly used formula in factorization. This knowledge focuses on the memorization and application of the perfect square formula. The difficulty is to understand the characteristics of the formula (such as the understanding of the coefficient of the primary term of the product in the formula).

Question 1: {(a+b) 2-(a-b) 2} 2={(a 2+b 2+2ab)-(a 2+b 2-2ab)) 2=(4ab) 2=16a 2b 2

Question 2: (x+2y) 2+(2x-y) 2+(3x-4y) 2=(x 2+4y 2+4xy)+(4x 2+y 2-4xy)+(9x 2+16y 2-24xy).

14x^2+21y^2-24xy

Question 3: (2x+3y) 2-(4x-9y)(4x+9y)+(2x-3y) 2

4x^2+9y^2+12xy)-(16x^2-81y^2)+(4x^2+9y^2-12xy)=-8x^2+99y^2

Question 4: The square of known (z-x) is -4(x-y)(y-z)=0, and x-2y+z=0 is verified

z-x)^2-4（x-y)(y-z)=0

z^2+x^2-2xz)-(4xy-4xz-4y^2+4yz)=0

z^2+x^2+2xz-(4xy-4y^2+4yz) =0

z+x)^2+4y^2-4xy-4yz =0

z+x-2y)^2=0

x-2y+z=0

6. It cannot be said that it is in the human body.

According to the formula.

a-b)²=a²-2ab+b²

So multiply by 2

14x 2+21y 2 is obtained by merging similar terms.

The formula for the perfect square formula is (a+b) 2=a 2+2ab+b 2, so 24xy is 3*4*2, and the last step is to open the brackets to calculate.

The perfect square formula (a+b) 2=a2+b 2+2ab

2*3x*4y=24xy

14x 2+21y 2 is obtained by merging similar terms.

xy

5. (a b) -2a b + (ab ) 4x +12x+9-x +4x-4=3x +16x+5(x -1) =(x) -2x +1 (Note: I can't play to the fourth power).

6. Original formula = 4a +4a + 1-4a -2 + 3 = 4a +4 when a = 2.

Original = 4 2 = 16

7. Original formula = 2 (m + 2mn + n ) -6 = 2 (m + n) -6 when m + n = 3.

Original = 2 3 -6 = 12

8. Let x-y=a, y-z=b, then x-z=a+b original formula = (x-z) -4(x-y)(y-z)=(a+b) -4ab=a +2ab+b -4ab=a -2ab+b =(a-b) =0

i.e. (x-y-y+z) =(x-2y+z) =0 x-2y+z=0

1,72,-6xy,3y/2

5（a²b-ab²）²=(a²b)²-2(a²b)(ab²)+ab²)²

2x+3）²-x-2）²=(2x+3-x+2)(2x+3+x-2)=(x+5)(3x+1)=3x²+16x+5

x+1）（x-1）（x²-1）=（x²-1）²

6（2a+1）²-2(2a+1)+3=（2a+1）²-2(2a+1)+1+2=（2a+1-1)²+2=4a²+2

7 2m²+4mn+2n²-6=2(m+n)²-6=18-6=12

8（z-x）²-4（x-y）（y-z）=(a+b)²-4ab=a²-2ab-b²=(a-b)²=[(x-y)-(y-z)]²=(x-2y+z)²=0

x-2y+z=0

Because word is not familiar with the third and fourth powers, can you draw it yourself?

a+b)^2=a^2+2ab+b^2

a-b)^2=a^2-2ab+b^2

a+b)^2

a+b)(a+b)

a^2+ab+ab+b^2

a^2+2ab+b^2

a-b)^2

a-b)(a-b)

a^2-ab-ab+b^2

a^2-2ab+b^2

Remember the head square, tail square, twice the head and tail put **, and then write + - according to the middle symbol

a+b+c) - (a-b+c) squared = (a+b+c+a-b+c)(a+b+c-a+b-c) = (2a+2c) multiplied by 2b=4ab+4bc

One. Fill a vacancy.

1.(a-b)(a-b)=4,ab=, then (a+b)(a+b)= (a-b) +4ab=6

2.(x+y)(x+y)=9,(x-y)(x-y)=5,then xy= [x+y) -x-y) ] 4=1

x+1)²+y-3)²=0

Then x = -1 and y = 3

Two. Short Calculation ==(

Recipe the original formula.

x²+4x+4+y²-6x+9=0

x+2)²+y-3)²=0

According to the nature of non-negative numbers, the sum of two non-negative numbers is 0, then both non-negative numbers are 0, so x=-2, y=3

x to the yth power.

It is to the 3rd power of (-2) = -8