\(x^2+y^2+2x+2y+2\left(x+1\right)\left(y+1\right)+2\)

\(=x^2+2x+1+y^2+2y+1+2\left(x+1\right)\left(y+1\right)\)

\(=\left(x+1\right)^2+2\left(x+1\right)\left(y+1\right)+\left(y+1\right)^2\)

\(=\left(x+1+y+1\right)^2\)

\(=\left(x+y+2\right)^2\)

\(=\left(x-y\right)\left(x+y\right)\)

= ( x-y).(x+y)

xy⁵  -5xy⁴+10xy³-10xy²+5xy-1

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

\(\left(x^2+y^2\right)\left(x^2-y^2\right)\)

Dựa vào hằng đẳng thức thứ 3 : (A + B)(A - B) = A² - B²

=> \(\left(x^2+y^2\right)\left(x^2-y^2\right)=\left(x^2\right)^2-\left(y^2\right)^2=x^4-y^4\)

( x² + y² )( x² - y² )

= ( x² )² - ( y² )

= x⁴ - y⁴

2/ \(\left(a+b\right)^k\Rightarrow k+1\left(so-hang\right)\)

\(\Rightarrow n+6+1=17\Rightarrow n=10\)

6/ \(\left(2a-1\right)^6=\sum\limits^6_{k=0}C^k_6.2^{6-k}.\left(-1\right)^k.a^{6-k}\)

\(\Rightarrow tong-3-so-hang-dau=C^0_6.2^6+C^1_6.2^5.\left(-1\right)+C^2_6.2^4.\left(-1\right)^2=...\)

7/ \(\left(x-\sqrt{y}\right)^{16}=\left(x-y^{\dfrac{1}{2}}\right)^{16}\)

\(\Rightarrow tong-2-so-hang-cuoi=C^{16}_{16}+C^{15}_{16}=...\)

a) (x² + 2)²

= (x²)² + 2.x².2 + 2²

= x⁴ + 4x² + 4

b) (x + y + z)²

= [(x + y) + z]²

= (x + y)² + 2(x + y).z + z²

= x² + 2xy + y² + 2xz + 2yz + z²

= x² + y² + z² + 2xy + 2xz + 2yz

sos

a,

   (\(x^2\) + 2)² 

= (\(x^2\))² + 2.\(x^2\).2 + 2² 

= \(x^4\) + 4\(x^2\) + 4

b, (\(x\) + \(y\) + z)²

=  (\(x\) + y)² + 2(\(x+y\))z + z²

= \(x^2\) + 2\(xy\) + y² + 2\(xz\) + 2yz + z²