Thực hiện phép tính sau:
a) 3y2(2y - 1) + y - y(1 - y + y2) - y2 + y;
b) 2x2.a - a(1 + 2x2) - a - x(x + a);
c) 2p. p2 -(p3 - 1) + (p + 3). 2p2 - 3p5;
d) -a2(3a - 5) + 4a(a2 - a)
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\(A=\left[6y^3-3y^2+y+1\right]-y-y^2-y^3-y^2\)
\(=5y^3-5y^2+1\)
\(B=2ax^2-2x^2-a-a+x^2+ax=2ax^2-x^2-2a+ax\)
\(C=\left(p^3+1+2p^3+6p^2-2p^3\right)\cdot3p^2-3p^5\)
\(=\left(p^3+6p^2+1\right).3p^2-3p^5=18p^4+3p^2\)
1/2. x 2 y 2 (2x + y)(2x – y)
= 1/2. x 2 y 2 (4 x 2 – 2xy + 2xy – y 2 )
= 1/2. x 2 y 2 (4 x 2 – y 2 )
= 1/2. x 2 . y 2 .4 x 2 + 1/2. x 2 y 2 . (- y 2 )
= 2 x 4 y 2 - 1/2. x 2 y 4
\(a,=10x^3-5x^2+5x\\ b,=x^3+27\\ c,=\dfrac{5}{2}xy-1-\dfrac{1}{2}y\\ d,=\left(2x^3-10x^2-11x^2+55x+12x-60\right):\left(x-5\right)\\ =\left[2x^2\left(x-5\right)-11x\left(x-5\right)+12\left(x-5\right)\right]:\left(x-5\right)\\ =2x^2-11x+12\)
\(a,\left(x^3+5x^2-2x+1\right)\left(x-7\right)\\ =x^4-7x^3+5x^3-35x^2-2x^2+14x+x-7\\ =x^4-2x^3-37x^2+15x-7\\ b,\left(2x^2-3xy+y^2\right)\left(x+y\right)\\ =2x^3+2x^2y-3x^2y-3xy^2+xy^2+y^3\\ =2x^3-x^2y-2xy^2+y^3\\ c,\left(x-2\right)\left(x^2-5x+1\right)-x\left(x^2+11\right)\\ =x^3-5x^2+x-2x^2+10x--x^3-11x\\ =x^3-7x^2\\ d,x\left(1-3x\right)\left(4-3x\right)-\left(x-4\right)\left(3x+5\right)\\ =x\left(4-15x+9x^2\right)-\left(3x^2-7x-20\right)\\ =4x-15x^2+9x^3-3x^2+7x+20\\ =9x^3-18x^2+11x+20\)
a) \(=6a-3+15-5a=a+12\)
b) \(=25x-12x+4+35-14x=-x+39\)
d) \(=2ab+8a^2-b^2-4ab+2ab-6a^2=2a^2-b^2\)
e) \(=x+x^2-x^3+x^4-x^5+1+x-x^2+x^3-x^4=-x^5+2x+1\)
f) \(=6y^3-3y^2+y-y+y^2-y^3-y^2+y=5y^3-3y^2+y\)
a) 3( 2a -1) +5( 3-a)
= 3. 2a -3.1 +5. 3- 5.a
= 6a -3+ 15-5a
=(6a -5a )+ (-3+ 15)
b) 25x - 4(3x - 1) +7(5 - 2x)
= 25x -4.3x + 4.1 + 7.5 - 7.2
=25x - 12x + 4 +35 - 14x
= (25x-12x-14x)+(4+35)
= -x=39
c) -12x3 -x1-2x-18x2
= -36x-x-2x-36x
= -75x
d) (2a-b)(b+4a)+2a(b-3a)
= 2ab+2a4a-bb-b4a+2ab-2a3b
= 2ab+8a2-b2-4ab+2ab-6a2
=(2ab-4ab+2ab)+(8a2-6a2)-b2
= 2a2-b2
e) (x+1)(2+x-x2+x3-x4)
= (x+1)(2-2x)
= x2-x2x+1.2-1.2x
=(2x-2x)-2x2+2
= -2x2+2
Lời giải:
a) (x2 + 2xy + y2) : (x + y)
= (x + y)2 : (x + y)
= x + y
b) (125x3 + 1) : (5x + 1)
= [(5x)3 + 1] : (5x + 1)
= (5x + 1)[(5x)2 – 5x + 1]] : (5x + 1)
= (5x)2 – 5x + 1
= 25x2 – 5x + 1
c) (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
\(a,=4x^2+12xy+9y^2\\ b,=25x^2-10xy+y^2\\ d,=4x^2+4xy^2+y^4\\ e,=9x^4-12x^2y+4y^2\\ g,=x^3+64\)
a) \(x^2y\left(5xy-2x^2y-y^2\right)\)
\(=5x^3y^2-2x^4y^2-x^2y^3\)
b) \(\left(x-2y\right)\left(2x^3+4xy\right)\)
\(=2x^4+4x^2y-4x^3y-8xy^2\)