The operation of integers in the first mathematics of junior high school, and the operation formula

1.Because a 2+b 2+2ab=(a+b) 2, inside the parentheses is, ab a 4+2b

or a 2 + b 2-2ab = (a-b) 2 so inside the parentheses is, -ab a 4-2b

2.(2mn)^2+(m^2-n^2)^24m^2*n^2+(m^2)^2+(n^2)^2-2m^2*n^2(m^2)^2+(n^2)^2+2m^2*n^2(m^2+n^2)^2

x-2)^2=0

then x=2x 3=2 3=8

Left = (1 4a) 2 + 2 * 1 4a * 2b + (2b) 2 = (1 4a + 2b) 2

Original = 4m 2n 2+m 4+n 4-2m 2n 2=m 4+n 4+2m 2n 2=(m 2+n 2) 2

It is known that (x-2) 2=0 so x-2=0 x=2 then x 3=8

Sum of squares formula.

ab,(1/4a+2b)^2

m^2+n^2)^2

x=2,x 3=8

Replace * to the 2nd power.

Common; （a+b）*=a*+2ab*+b*：（a-b）*=a*-2ab*+b*

Full square formula).

a* times a* = a*+*

Note that it does not have to be 2 power, the bases must be equal and the exponents are added) a* divided by a*=1

Same as above, but note that it stands to reason that the power of 0 of any number should be 0, but to be honest, it is 1, and the division is the exponential subtraction).

a+b+c)*=This is the multiplication of 2 such equations: a*+c*+b*+2ab+2ac+2bc

ab）*=a*b*

a-b）（a+b）=（a-b）*

Note that regardless of whether the plus sign is done or right, the result is minus).

It's tiring! How to play to the 2nd power.

;（a+b）*=a*+2ab*+b*：（a-b）*=a*-2ab*+b*

Full square formula).

a* times a* = a*+*

Note that it does not have to be 2 power, the bases must be equal and the exponents are added) a* divided by a*=1

Same as above, but note that it stands to reason that the power of 0 of any number should be 0, but to be honest, it is 1, and the division is the exponential subtraction).

a+b+c)*=This is the multiplication of 2 such equations: a*+c*+b*+2ab+2ac+2bc

ab）*=a*b*

a-b）（a+b）=（a-b）*

the formula for the operation of integers; We can replace it with numbers and people. For example, the area of a trapezoid: s = (top bottom, bottom bottom) height 2

As; 20 pieces of wood are stacked in a trapezoidal shape;

Use the formula s=(top bottom, bottom bottom) high 2

There are 2 at the bottom, 8 at the bottom, and 4 at the high. substitution formulas;

s=（2＋8）×4÷2

s=10×4÷2

s=20

Let's solve it in the simplest way:

Find out the integer they are close to first:

Then find them.

The integer of the broom approach:

30) to the power of 50.

Greater than (40) to the power of 40.

Greater than (50) to the power of 30.

33 to the 55th power.

Greater than 44 to the power of 44.

Greater than 55 to the power of 33.

Bonus points!

No matter what grade the formula is, it takes several steps to be able to use it:

One: Familiarize yourself with the formula.

Two: Find a few similar questions to do.

Three: Do more difficult questions.

Four: Memorize the formula.

itiseasy!

Solution: Because x+2y-1=0, x+2y=1

3 to the 2x power of 81 to the power of y-8=9 xx9 (2y)-8=9 (x+2y)-8=9-8=1

Explanation: 3 to the 2x power becomes 9 to the x power, 81 becomes 9 2, use the inverse operation of the power of the square and the multiplication operation of the same base meter, and then substitute it as a whole.

Compare sizes. 7 to the 60th power and 48 to the 30th power: This problem can be converted in this way to the 60th power of 7 can be equal to the 30th power of 7 times the 30th power of 7, then it can become 49 to the 30th power, so the 60th power of 7 is greater than the 30th power of 48.

3 to the 2x power 81 to the y power -8

9 to the x power 9 to the 2y power of 8

9 to the power of (x+2y) -8

9-8 (x+2y-1=0 to x+2y=1) = 60 power of 17 = 30 power of 49.

It is larger than the 48 to the 30th power.

81 can be written as 3 to the 4th power x+2y=1

The above equation is equal to the power of (2x+4y) of 3 -8=1

7 to the 60th power = 49 to the 30th power and 48 to the 30th power.

Original=[( x(a2+

x(a2+

Note: The 2 after a means to the 2nd power, and the 2 next to the parentheses is also to the 2nd power.

Just combine the first and third formulas, use the squared difference formula, and then use the squared difference formula again. This kind of question is this trick.

4m^2+8mn+4n^2

Let the odd number be n, so n*(n+2)+1

Let n+1=a

So (a+1)*(a-1)+1

Perfect squared difference formula.

a^2-1+1=a^2

Because n is an odd number.

So n-1 is an even number.

x=5y=2

From the known knowledge, xy is less than the 9th power of the equal Sun Socks in 9, 2 = 5129 to the 4th power = 6561 and greater than 2x9y

Therefore, the value range of y is 123

Because x is not equal to 0, 2x9y is an even number.

So y=2, so the dust excites x=5

This number is 2592

Method 1: Balance the first side wheel with an equation: x 24xy 26y

x^2y^24x6y

With the second Fang Yun lead letter Cheng Lian, the solution. x

Y method 2: In Equation 2. x3y

Substitute into Equation 1. Get. 3y

y-3)^2

4y2)(2y

Solution. yx