A=(a+1)(a+2)(a^2+4)(a-1)(a^2+1)(a-2)

A =(a+1)(a-1)(a+2)(a-2)(a^2+4)(a^2+1)

A =(a^2-1)(a^2+1)(a^2-4)(a^2+4)

A =(a^4-1)(a^4-16)

A =\(a^{16}-16\cdot a^4-a^4+16\)

A =\(a^{16}-17\cdot a^4+16\)

B=(a+2b-3c-d)(a+2b+3c+d)

B=[(a+2b)^2 - (3c +d)^2]

B=[a^2+4ab+4b^2-(9c^2+6cd+d^2)]

B=a^3+4ab+4b^2 - 9c^2 - 6cd - d^2

C=(1-x-2x^3+3x^2)(1-x+2x^3-3x^2)

C=[(1-x)^2-(2x^3-3x^2)^2]

C=[(1-2x+x^2) - (4x^6-12x^5+9x^4)]

C=[1-2x-x^2-4x^6+12x^5-9x^4]

C=-4x^6+12x^5-9x^4-x^2-2x+1

D=(a^6-3a^3+9)(a^3+3)

D=a^9+27

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Đặt a+2b là x; 3c+d là y

Ta có (x-y)(x+y)=x²-y²

                         =(a+2b)²-(3c+d)²

                         =a²+4b²-9c²-d²+4ab-6cd

B = ( a + 2b - 3c - d )( a + 2b + 3c + d )

B = [ ( a + 2b ) - ( 3c + d ) ][ ( a + 2b ) + ( 3c + d ) ]

B = ( a + 2b )² - ( 3c + d )²

B = a² + 4ab + 4b² - ( 9c² - 6cd + d² )

B = a² + 4ab + 4b² -  9c² + 6cd - d² 

\(\left(a^2-1\right)\left(a^2-a+1\right)\left(a^2+a+1\right)=\left(a-1\right)\left(a^2+a+1\right)\left(a+1\right)\left(a^2-a+1\right)\)

\(=\left(a^3-1\right)\left(a^3+1\right)=a^6-1\)

(125x3 + 1) : (5x + 1)

= [(5x)3 + 1] : (5x + 1)

= (5x + 1)[(5x)2 – 5x + 1]] : (5x + 1)

= (5x)2 – 5x + 1

= 25x2 – 5x + 1

(x2 – 2xy + y2) : (y – x)

= (x – y)2 : [-(x – y)]

= -(x – y)

= y – x

Hoặc (x2 – 2xy + y2) : (y – x)

= (y2 – 2yx + x2) : (y – x)

= (y – x)2 : (y – x)

= y – x

(x2 + 2xy + y2) : (x + y)

= (x + y)2 : (x + y)

= x + y

=2x-1