\(a^2+b^2=2\left(8+ab\right)\)

=> \(a^2-2ab+b^2=16\)

=> \(\left(a-b\right)^2=16\)

=> a - b = 4 hoặc a - b = -4

Mà a < b

=> a - b < 0

=> a - b = -4

=> a = - 4 + b

Khi đó

\(P=\left(b-4\right)^2\left(-4+b\right)-b^2\left(b-1\right)-3\left(-4+b\right)\left(-4+1\right)+64\)

\(=\left(b^2-8b+16\right)\left(-4+b\right)-b^3+1-9\left(b-4\right)+64\)

\(=-4b^2+32b-64+b^3-8b^2+16b-b^3+1-9b+36+64\)

\(=-12b^2+49b+37\)

Chịu rồi! tách được thì tách không tách được chắc sai :v

\(A=a^3+a^2-b^3+b^2+ab-3a^2b+3ab^2-3ab=\left(a^3-b^3-3a^2b+3ab^2\right)+\left(a^2-2ab+b^2\right)=\left(a-b\right)^3+\left(a-b\right)^2\)

\(=\left(a-b\right)\left(a-b+1\right)\)

phân tích thành nhân tử rồi đó. ngta cho a-b= bao nhiêu thì mới tính 

a) \(a^2+2a+b^2-2b-2ab=\left(a-b\right)^2+2\left(a-b\right)\)

Thay a-b=7 vào trên ta được:

7^2+2*7=63

\(2x^2+y^2+9=6x+2xy\Leftrightarrow\left(x^2-2xy+y^2\right)+\left(x^2-6x+9\right)=0\)

\(\Leftrightarrow\left(x-y\right)^2+\left(x-3\right)^2=0\Leftrightarrow\hept{\begin{cases}x-3=0\\x-y=0\end{cases}}\Leftrightarrow x=y=3\)

\(\Rightarrow A=x^{2019}.y^{2020}-x^{2020}.y^{2019}+\frac{1}{9xy}=\frac{1}{27}\)

Ta có \(A=a^2.\left(a+1\right)-b^2.\left(b-1\right)+ab-3ab.\left(a-b+1\right)\)

\(=a^3+a^2-b^3+b^2+ab-3ab-3.a^2.b+3a.b^2\)

\(=a^3-3a^2b+3ab^2-b^3+a^2-2ab+b^2\)

\(=\left(a-b\right)^3+\left(a-b\right)^2\)

\(=7^3-7^2=294\)

a,= a\(^2\)+2a+b\(^2\)-2b-2ab+37

=a\(^2\)-2ab+b\(^2\)+2a-2b+37

=(a-b)\(^2\)+2(a-b)+37

⇒5\(^2\)+2.5+37= 25+10+37= 72

b,= a\(^3\)+a\(^2\)-b\(^3\)+b\(^2\)+ab-3a\(^2\)b+3ab\(^2\)-3ab-95

=a\(^3\)-3a\(^2\)b+3ab\(^2\)-b\(^3\)+a\(^2\)-2ab+b\(^2\)-95

=(a-b)\(^3\)+(a-b)\(^2\)-95

⇒5\(^3\)+5\(^2\)-95= 125+25-95= 60

Ta có: \(M=a^3+b^3+3ab\left(a^2+b^2\right)+6a^2b^2\cdot\left(a+b\right)\)

\(\Leftrightarrow M=\left(a+b\right)\left(a^2-ab+b^2\right)+3ab\left(a^2+b^2\right)+6a^2b^2\)

\(\Leftrightarrow M=a^2-ab+b^2+3ab\left(a^2+2ab+b^2\right)\)

\(\Leftrightarrow M=a^2-ab+b^2+3ab\cdot\left(a+b\right)^2\)

\(\Leftrightarrow M=a^2-ab+3ab+b^2\)

\(\Leftrightarrow M=\left(a+b\right)^2=1^2=1\)

Vậy: Khi a+b=1 thì M=1