\(\left(x^{2n}+x^ny^n+y^{2n}\right)\left(x^n-y^n\right)\left(x^{3n}+y^{3n}\right)\)

\(=\left(x^{3n}-y^{3n}\right)\left(x^{3n}+y^{3n}\right)\)

\(=x^{6n}-y^{6n}\)

Bài làm :

\(a,\left(8-5x\right)\left(x+2\right)+4\left(x-2\right)\left(x+1\right)+2\left(x-2\right)\left(x+2\right)+10\)

\(=8x+16-5x^2-10x+\left(4x-8\right)\left(x+1\right)+2\left(x^2-2^2\right)+10\)

\(=8x+16-5x^2-10x+4x^2+4x-8x-8+2x^2-8+10\)

\(=\left(8x-10x+4x-8x\right)+\left(-5x^2+4x^2+2x^2\right)+\left(16-8-8+10\right)\)

\(=-6x+x^2+10\)

a)\(\left(8-5x\right)\left(x+2\right)+4\left(x-2\right)\left(x+1\right)+2\left(x-2\right)\left(x+2\right)+10\)\(=8x+16-5x^2-2+4x-8x-8+2x-4x-4+10\)\(=\left(8x+4x-8x+2x-4x\right)+\left(16-2-8-4+10\right)+5x^2\)

\(=2x+12+5x^2\)

b)\(4\left(x-1\right)\left(x+5\right)-\left(x+2\right)\left(x+5\right)-3\left(x-1\right)\left(x+2\right)\)

\(=4x-4x-20-\left[x^2+5x+2x+10\right]-3\left[x^2+2x-1x-2\right]\)

\(=4x-4x-20-x^2-5x-2x-10-3x^2-6x+3x+6\)

\(=\left(4x-4x-5x-2x-6x+3x\right)+\left(-20-10+6\right)+\left(-x^2-3x^2\right)\)

\(=-10x-24-4x^2\)

c)\(\left(x^{2n}+x^ny^n+y^{2n}\right)\left(x^n-y^n\right)\left(x^{3n}+y^{3n}\right)\)

Xét tích \(\left(x^{2n}+x^ny^n+y^{2n}\right)\left(x^n-y^n\right)\Leftrightarrow\left(x^n\right)^3-\left(y^n\right)^3=x^{3n}-y^{3n}\)

Thay vào bt đã cho ta có \(\left(x^{3n}-y^{3n}\right)\left(x^{3n}+y^{3n}\right)\)

\(\Leftrightarrow\left(x^{3n}\right)^2-\left(y^{3n}\right)^2=x^{6n}-y^{6n}\)

a) ( 8 - 5x )( x + 2 ) + 4( x - 2 )( x + 1 ) + 2( x - 2 )( x + 2 ) + 10

= -2x - 5x² + 16 + 4( x² - x - 2 ) + 2( x² - 4 ) + 10

= -2x - 5x² + 16 + 4x² - 4x - 8 + 2x² - 8 + 10

= x² - 6x + 10

b) 4( x - 1 )( x + 5 ) - ( x + 2 )( x + 5 ) - 3( x - 1 )( x + 2 )

= 4( x² + 4x - 5 ) - ( x² + 7x + 10 ) - 3( x² + x - 2 )

= 4x² + 16x - 20 - x² - 7x - 10 - 3x² - 3x + 6

= 6x - 24 = 6( x - 4 )

c) ( x²ⁿ + xⁿyⁿ + y²ⁿ )( xⁿ - yⁿ )( x³ⁿ + y³ⁿ )

= [ ( xⁿ )³ - ( yⁿ )³ ]( x³ⁿ + y³ⁿ )

= ( x³ⁿ - y³ⁿ )( x³ⁿ + y³ⁿ )

= ( x³ⁿ )² - ( y³ⁿ )² = x⁶ⁿ - y⁶ⁿ