Toán Lớp 7: 1) 6x^2 -2x (3x+3/2) 2) (x^2 + 4x) (2x^3 -8x^2 +32) 3) (5x^3 -x^2 +2x -3) (4x^2 -x+2) 4) (25x^2 +10xy +4y^2) (5x-2y) 5) 3x^2 -2x (5-1,5

Question

Toán Lớp 7:  1) 6x^2 -2x (3x+3/2) 2) (x^2 + 4x) (2x^3 -8x^2 +32) 3) (5x^3 -x^2 +2x -3) (4x^2 -x+2) 4) (25x^2 +10xy +4y^2) (5x-2y) 5) 3x^2 -2x (5-1,5x) +10 6) 2x^4 -5x^3 +4x^2 (-1/2x^2 +5/4x +1) 7) 7x (4y-x) + 4y (y-7x) -2 (2y^2-3,5x) 8) 1/2 x^3 (4x^2 -6x +1/2) - (x^3 -1/2x^2-1/8x) 2x^2 9) (x^2 -2 ) ( x^2+x -1)  -x (x^3 +x^2 -3x -2) 10) (3x+2y -1) (x+5) (x-2) 2y

tongtung · Answer

***Lời giải***

1)

6x^2 -2x (3x+3/2)
=6x^2 -6x^2-3x
=-3x

2)

(x^2 + 4x) (2x^3 -8x^2 +32)
=x^2 (2x^3 -8x^2 +32)+4x (2x^3 -8x^2 +32)
=2x^5-8x^4+32x^2+8x^4-32x^3+128x
=2x^5-32x^3+32x^2+128x

3)

(5x^3 -x^2 +2x -3) (4x^2 -x+2)
=4x^2(5x^3 -x^2 +2x -3)-x(5x^3 -x^2 +2x -3)+2(5x^3 -x^2 +2x -3)
=20x^5-4x^4+8x^3-12x^2-5x^4+x^3-2x^2+3x+10x^3-2x^2+2x-6
=20x^5-9x^4+19x^3-16x^2+5x-6

4)

(25x^2 +10xy +4y^2) (5x-2y)
=5x(25x^2 +10xy +4y^2)-2y(25x^2 +10xy +4y^2)
=125x^3+50x^2y+20xy^2-50x^2y-20xy^2-8y^3
=125x^3-8y^3

5)

3x^2 -2x (5-1,5x) +10
=3x^2-10x+3x^2+10
=6x^2-10x+10

6)

2x^4 -5x^3 +4x^2 (-1/2x^2 +5/4x +1)
=2x^4 -5x^3 -2x^4+5x^3+4x^2
= 4x^2

7)

7x (4y-x) + 4y (y-7x) -2 (2y^2-3,5x)
=28xy-7x^2+4y^2-28xy-4y^2+7x
=-7x^2+7x

8)

1/2 x^3 (4x^2 -6x +1/2) – (x^3 -1/2x^2-1/8x) 2x^2
=2x^5-3x^4+1/4x^3-2x^5+x^4+1/4x^3
=-2x^4+1/2x^3

9)

(x^2 -2 ) ( x^2+x -1) -x (x^3 +x^2 -3x -2)
=x^2( x^2+x -1)-2( x^2+x -1)-x (x^3 +x^2 -3x -2)
=x^4+x^3-x^2-2x^2-2x+2-x^4-x^3+3x^2+2x
=2

10)

(3x+2y -1) (x+5) (x-2) 2y
=(2xy-4y)(x+5)(3x+2y -1)
=[2xy(x+5)-4y(x+5)](3x+2y -1)
=(2x^2y+10xy-4xy-20y)(3x+2y -1)
=(2x^2y+6xy-20y)(3x+2y -1)
=3x(2x^2y+6xy-20y)-(2x^2y+6xy-20y)+2y(2x^2y+6xy-20y)
=6x^3y+18x^2y-60xy-2x^2y-6xy+20y+4x^2y^2+12xy^2-40y^2
=6x^3y+16x^2y-66xy+20y+4x^2y^2+12xy^2-40y^2

maitrucloan · Answer

Giải đáp+Lời giải và giải thích chi tiết:     1) 6x^2-2x(3x+3/2)   =6x^2-6x^2-3x   =-3x   2) (x^2+4x)(2x^3-8x^2+32)   =x^2 . (2x^3-8x^2+32)+4x.(2x^3-8x^2+32)   =2x^5-8x^4+32x^2+8x^4-32x^3+128x   =2x^5-(8x^4-8x^4)-32x^3+32x^2+128x   =2x^5-32x^3+32x^2+128x   3) (5x^3-x^2+2x-3)(4x^2-x+2)   = 4x^2 . (5x^3-x^2+2x-3)-x. (5x^3-x^2+2x-3)+2.(5x^3-x^2+2x-3)   =20x^5-4x^4+8x^3-12x^2-5x^4+x^3-2x^2+3x+10x^3-2x^2+4x-6   =20x^5+(-4x^4-5x^4)+(8x^3+x^3+10x^3)-(12x^2+2x^2+2x^2)+(4x+3x)-6   =20x^5-9x^4+19x^3-16x^2+7x-6   4) (25x^2+10xy+4y^2)(5x-2y)   =5x.(25x^2+10xy+4y^2)-2y.(25x^2+10xy+4y^2)   =125x^3+50x^2y+20xy^2-50x^2y-20xy^2-8y^3   =125x^3-(50x^2y-50x^2y)+(20xy^2-20xy^2)-8y^3   =125x^3-8y^3   5) 3x^2-2x(5-1,5x)+10   =3x^2-10x+3x^2+10   =6x^2-10x+10   6) 2x^4-5x^3+4x^2(-1/2x^2+5/4x+1)   =2x^4-5x^3-2x^4+5x^3+4x^2   =4x^2   7) 7x(4y-x)+4y(y-7x)-2(2y^2-3,5x)   =28xy-7x^2+4y^2-28xy-4y^2+7x   =-7x^2+7x   8) 1/2x^3(4x^2-6x+1/2)-(x^3-1/2x^2-1/8x)2x^2   =2x^5-3x^4+1/4x^3-2x^5+x^4+1/4x^3   =-2x^4+1/2x^3   9) (x^2-2)(x^2+x-1)-x(x^3+x^2-3x-2)   =x^4+x^3-x^2-2x^2-2x+2-x^4-x^3+3x^2+2x   =2   10) (3x+2y-1)(x+5)(x-2)2y   = [(3x+2y-1)(x+5)][(x-2)2y]   =(3x^2+15x+2xy+10y-x-5)(2xy-4y)   =(3x^2+14x+2xy+10y-5)(2xy-4y)   =2xy(3x^2+14x+2xy+10y-5)-4y(3x^2+14x+2xy+10y-5)   =6x^3y+28x^2y+4x^2y^2+20xy^2-10xy-12x^2y-56xy-8xy^2-40y^2+20y   =6x^3y+16x^2y+4x^2y^2+12xy^2-66xy-40y^2+20y