Middle School Mathematics 1 m 2 n 2 2 4m 2n 2 2 a 2 b 2 2b 1

Hello life, the solution is as follows:

1)(m 2+n 2) 2-4m 2n 2 solution: =m 4+2m 2n 2+n 4-4m 2n 2m 4-2m 2n 2+n 4

m^2-n^2)^2

m+n)^2(m-n)^2

2）a^2-b^2-2b-1

Solution: =a 2-(b 2+2b+1).

a^2-(b+1)^2

a+b+1)(a-b-1)

If you don't understand something, you can ask. If that's okay, don't forget the answer!

Make use of the squared difference formula:

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

and the perfect square formula:

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

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

m^2+n^2）^2-4m^2n^2

m^4+2m^2n^2+n^4-4m^2n^2m^4-2m^2n^2+n^4

m^2-n^2)^2

m+n)^2(m-n)^2

a^2-b^2-2b-1

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

a^2-(b+1)^2

a+b+1)(a-b-1)

If you don't understand, please ask. If not.

hi!For ease of understanding, m 2 can be seen as a and n 2 as b

So (1)(m2+n2) 2-4m2n2=(a+b) 2-4ab=(a-b) 2

Because (a+b) 2=a 2+2ab+b 2 (a-b) 2=a 2-2ab+b 2 is just 4ab worse, isn't it?

So the original formula = (m2-n2) 2

Question 2: a 2-b 2-2b-1=a 2-(b 2+2b+1) [separate the latter first].

a^2-(b+1)^2【a^2-b^2=(a+b)(a-b)】

a+b+1)(a-b-1)

Got it? To summarize the above with the perfect square formula and a 2-b 2=(a+b)(a-b).

(m-n) 2 =8, m2 -2mn+n 2 =8 , (yard answer m+n) 2 =2, Antkai.

m 2 +2mn + n 2 =2 ,+de,2m 2 +2n 2 =10,m 2 +n 2 =5 Chi Hui.

Therefore, c

(m-n) opening 2

10, (m+n) pure side-lift 2

2，m2n2

2mn=10, do bi m2

N22mn=2 then m2n2

Therefore, c

Solution: m+n=2, mn=-3

So: Solution (1).

2（m+n）-2[mn+(m+n)]-3[2(m+n)-3mn]=2*2-2(-3+2)-3(2*2+3*3)=4+2-39

Solution (2) 2(m+n)-2[mn+(m+n)]-3[2(m+n)-3mn]=2(m+n)-2mn-2(m+n)-6(m+n)+9mn=-6(m+n)+7mn

So the original formula = -6*2+7*(-3).

Substitute first and evaluate later:

By the absolute value of the property m+n-2

0, and (mn+3) 2 0,丨m+n-2丨+(mn+3) 2=0, then m+n-2=0, mn+3=0, substitute 2(m+n)-2[mn+(m+n)]-3[2(m+n)-3mn] to get the answer 33

Simplified and evaluated:

2（m+n）-2[mn+(m+n)]-3[2(m+n)-3mn]=-6（m+n)+7mn=－33

(2m+n)(2m-n)

2m)²-n²

4m²-n²

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Apply the squared difference formula.

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

If you still don't understand, you can ask me again.

From the meaning of the title:

m-n+2=0

2m+n+4=o

So: m-n=-2

2m+n=-4 (solve the system of equations).

m=-2 n=0

So: m n=(-2) 0=1

As a reminder, absolute values after squares are all non-negative.

As for 3, you can understand that 3*some non-negative number, then 3*(2m+n+4)=0, i.e., 2m+n+4=0

Then a system of binary linear equations is established.

Genus, that is. m-n+2=0

2m+n+4=0

Solution m=-2, n=0

And then you know.

The addition of two non-negative numbers is equal to zero, and only two of them can be zero at the same time, i.e., m-n+2=0, 2m+n+4=0 to obtain a system of binary linear equations about m,n, and the solution is m=-2, n=0, and the zero power of (-2) is equal to 0