\(A=\left(5x-1\right)+2\left(1-5x\right)\left(4+5x\right)\left(5x+4\right)^2\)

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

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

\(=\left(5x-1\right)\left(1-2\left(125x^3+300x^2+240x+64\right)\right)\)

\(=\left(5x-1\right)\left(1-250x^3-600x^2-480x-128\right)\)

\(=5x-1250x^4-3000x^3-2400x^2-640x-1+250x^3+600x^2+480x+128\)

\(=-1250x^4-2750x^3-1800x^2-110x+127\)

(Số hơi to)

\(B=\left(x-y\right)^3+\left(y+x\right)^3+\left(y-x\right)^3-3xy\left(x+y\right)\)

\(B=\left(x-y\right)^3+\left(y+x\right)^3-\left(x-y\right)^3-3xy\left(x+y\right)\)

\(B=\left(y+x\right)^3-3xy\left(x+y\right)\)

\(B=\left(x+y\right)\left[\left(x+y\right)^2-3xy\right]\)

\(B=\left(x+y\right)\left[x^2+2xy+y^2-3xy\right]\)

\(B=\left(x+y\right)\left(x^2-xy+y^2\right)\)

\(=x^3+y^3\)

Cái này bihf thường:

a.A=

a)\(P=\left(5x-1\right)+2\left(1-5x\right)\left(4+5x\right)+\left(5x+4\right)\)

   \(P=5x-1+5x+4+\left(2-10x\right)\left(4+5x\right)\)

   \(P=10x+3+8+10x-40x-50x^2\)

    \(P=-20x+11-50x^2\)

b)\(Q=\left(x-y\right)^3+\left(y+x\right)^3+\left(y-x\right)^3-3xy\left(x+y\right)\)

   \(Q=x^3-3x^2y+3xy^2-y^3+y^3+3y^2x+3yx^2+x^3+y^3-3y^2x+3yx^2-x^3-3x^2y+3xy^2\)

   \(Q=x^3+y^3\)

a) P = (5x - 1) + [(-2).(-1).(1-5x).(4+5x)] + (5x+4)^2 
= (5x - 1).[(-1)-2.(-1).(4+5x)] + (25x^2+40x+16) 
= [(5x - 1).(10x + 7)] + (25x^2+40x+16) 
= 50x^2 +35x - 10x - 7 + 25x^2+40x+16 
= 75x^2 + 65x -9 
b) Q = (x-y)^3 + (x+y)^3 + (y-x)^3 - [3xy(x+y)] 
Xét (x-y)^3 = x^3 - 3x^2y + 3xy^2 - y^3  = x^3 + 3x^2y + 3xy^2 + y^3  = y^3 - 3xy^2 + 3x^2y - x^3 
Do đó Q = (2x^3 + 6xy^2) + (y^3 - 3xy^2 + 3x^2y - x^3) - [3xy(x+y)] 
= (x^3 + 3xy^2 + 3x^2y + y^3) - 3x^2y - 3xy^2 
= x^3 + y^3

 a, P=(5x-1)+2(1-5x)(4+5x)+(5x+4)

=5x-1+2.(4-15x-5x²)+5x+4

=5x-1+8-30x-10x²+5x+4

=-10x²-20x+11

  b,Q=(x-y)^3 +(y+x)^3+ (y-x)^3 -3xy(x+y)

=x³-3x²y+3xy²-y³+y³+3x²y+3xy²+x³+y³-3y²x+3yx²-x³-3x²y-3xy²

=x³+y³

P=(5x-1).(1+4+5x)+(4+5x)(1-5x+1)

= (5x-1)(5x+5)+(4+5x)(2-5x)

=25x²+20x-5+8-25x²-10x

=10x+3

Q=x³-3x²y+3xy²-y³+x³+3x²y+3xy²+y³+y³-3y²x+3yx²-x³-3xy²-3x²y

=x³+y+3xy(x+y)=(x+y)³

a)

P=(5x−1)+2(1−5x)(4+5x)+(5x+4)²
P=(5x−1)²+2(1−5x)(4+5x)+(5x+4)²−(5x−1)²
P=(5x−1+5x+4)²−(5x−1)²
P=(5x−1+5x+4−5x+1)(5x−1+5x+4+5x−1

b)

Q= (x-y)^3 + (x+y)^3 + (y-x)^3 - [3xy(x+y)] 

(x-y)^3 = x^3 - 3x^2y + 3xy^2 - y^3 

(x+y)^3 = x^3 + 3x^2y + 3xy^2 + y^3 

(y-x)^3 = y^3 - 3xy^2 + 3x^2y - x^3 

Q= (2x^3 + 6xy^2) + (y^3 - 3xy^2 + 3x^2y - x^3) - [3xy(x+y)] 
= (x^3 + 3xy^2 + 3x^2y + y^3) - 3x^2y - 3xy^2 
Q= x^3 + y^3

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