Calculated with 7th grade multiplication formulas, 7th grade math multiplication formulas

1): Square difference formula: original formula = (y+3+3-y)(y+3-3+y)6*2y12y

2) Perfect squared: Original formula =-(1-x-y)(1-x-y)-(1-(x+y)) 2

1-2(x+y)+(x+y)^2)

1-2x-2y+x^2+2xy+y^2)-x^2-y^2-2xy+2x+2y-1

3) Square difference formula: original formula = (2b+a-1)(2b-(a-1))(2b) 2-(a-1) 2

4b^2-(a^2-2a+1)

4b^2-a^2+2a-1

4) Perfect Squared: Original = ((a-3b)+2) 2(a-3b) 2+4(a-3b)+4

a^2-6ab+9b^2+4a-12b+4a^2+9b^2-6ab+4a-12b+4

y2+6y+9-9+6y-y2=12y

x+y-1)(x+y-1)=-(x2+y2+1+2xy-2x-2y)=-x2+y2+1+2xy-2x-2y

4x2+20xy+25y2-4y2+20xy-25y2=40xy2b+a-1)(2b-(a-1))=4b2-(a-1)2=4b2-a2+2a-1

a2+9b2+4-6ab+4a-12b

That's all for the process, if you don't understand, ask me.

The trick of the power operation is that Yu Liang multiplies a number by itself, where the base number represents the number to be multiplied, and the exponent represents the number of times to be destroyed and shouted multiplied.

1. The expression of power

1. In mathematics, there are many ways to represent power, and the common superscript symbol ( ) can also be represented in the form of a function or a specific power operation symbol in the language.

2. Use superscript symbols: 2 3, read as 2 to the 3rd power; Use the function form: pow(2,3), which represents 2 to the third power; Use a specific power notation: 2**3, which means 2 to the 3rd power.

2. The nature of power

1. Multiplicative properties of power: For any real number a and positive integers m and n, there are the following multiplicative properties: a m*a n=a (m+n):

If two powers are multiplied and the base number is the same, the exponents are added; (a m) n=a (m*n): The power of a power number, multiplied by the base and the exponent.

2. The division property of power: for any real number a and positive integers m and n, there are the following division properties: a m a n = a (m-n): two power numbers are divided, and the base number is the same, then the exponent is subtracted.

3. Power property: For any real number a and positive integers m and n, there are the following power properties: (a m) n = a (m*n): the power of a power number, multiplying the base number and the exponent.

4. The power of the sock field to the zero power and the first square: for any real number a, there are the following properties: a 0=1: the zero power of any non-zero number is equal to: the first power of any non-zero number is equal to itself.

3. The method of calculating power

1. The value of the power calculation is generally carried out by multiplication. For example, calculate 2 to the 3rd power: 2 3 = 2 * 2 * 2 = 8.

2. In the actual calculation, the properties and laws of power can be used to simplify the calculation, for example: to calculate 2 4, you can first calculate 2 2 = 4, and then square 4 to get 2 4 = 16. Calculate 2 6, you can first calculate 2 3 = 8, and then square 8 to get 2 6 = 64.

Note s=(2+1)(2 squared +1)......2n square of 2 + 1) then (2-1) s = (2-1) (2 + 1) (2 square + 1) ......= (2 squared - 1) (2 squared + 1) ......

= (2n square of 2-1) (2n square of 2 + 1) = 4n square of 2-1

So s = (2 of 4n square-1) (2-1) = 2 of 4n square-1

=1+2+2^2+2^3+2^4+2^5+2^6+…2^(4n-1)

1+1+2+2^2+2^3+2^4+2^5+2^6+…2^(4n-1)-1

2+2+2^2+2^3+2^4+2^5+2^6+…2^(4n-1)-1

2^2+2^2+2^3+2^$+2^5+2^6+…2^(4n-1)-1

2×2^2+2^3+2^$+2^5+2^6+…2^(4n-1)-1

2×2^(4n-1)-1

2^4n-1

That's how it should be. ∵（2+1）(2^2+1)=1+2+2^2+2^3,(1+2+2^2+2^3)(2^4+1)=1+2+2^2+2^3+2^4+2^5+2^6+2^7

Original = 1+2+2 2+2 3+2 4+2 5+2 6+2 7+....+2^(4n-1)

In the end, of course, the simplest algorithm is upstairs.

Final result: (2 2n-1) (2 2n+1) = 2 4n-1

This problem is the law of finding the squared difference formula, and I don't know how I started with such a complex algorithm.

The squared difference formula is applied continuously.

2+1）（2^2+1）（2^4+1）……2^2n+1）=（2-1）（2+1）（2^2+1）（2^4+1）……2^2n+1）=(2^2-1）(2^2+1）（2^4+1）……2^2n+1）=（2^4-1）（2^4+1）……2^2n+1）

…=2^4n-1

Is it a sum or a recursive formula?

In addition, the landlord is not clear enough, is it 2 (2n)+1 ?

The original equation can be reduced to (m-7)(m+2)=0, so m=7 or m=-2

Just bring m=7 and m=-2 into the two questions.

Hope mine is helpful to you.

m is equal to -2 or 7 below you can calculate.

m 2-5m-14 = 0 can be reduced to (m-7) (m+2) = 0, of course, this is based on what you have learned about factoring.

In this way, m = 7 or -2. There should be a simple way, but once you have mastered the basics, it is the same if you are faster.

(1) Basic formula:

Square Difference Formula: (a+b)(a-b) = a -b Perfect Square Formula: (a b) =a 2ab+b Cube Sum Formula:

a+b)(a-ab+b)=a+b cubic variance formula: (a-b)(a+ab+b)=a-b (2) Supplementary formula:

x+a)(x+b)=x 2+(a+b)x+ab sum cubic formula: (a+b) =a +3a b+3ab +b difference cubic formula: (a-b) =a -3a b+3ab -b triple number and square formula:

a+b+c）²=a²+b²+c²+2ab+2bc+2ca

Basic Formula:

Perfect square formula: (a b)2=a2 2ab+b2, square difference formula: (a+b)(a b)=a2 b2 cube sum (difference) formula: (a b)(a2 ab+b2)=a3 b3 The common deformations of the perfect square method are:

1.(m+n) to the power of 2 is equal to 16,; The value of m to the power of 4 + n to the power of 4 is equal to 136

2: x square + x square is equal to 14,; x-x-x) squared is equal to 12

Answer: 1,(m-n) 2=m 2+n 2-2mn= --m 2+n 2=8+4=12, then (m+n) 2=m 2+n 2+2mn=12+4=16

m^4+n^4=(m^2+n^2)^2-2(mn)^2=144-2*2^2=136

The basic formula: perfect square formula: (a b)2=a2 2ab+b2, square difference formula: (a+b)(a-b)=a2-b2

Sum of cubes (difference) formula: (a b) (a2

ab+b2)=a3±b3

Common deformations of the perfect flat method are: