a) 3x³ + 6x²y

= 3x².(x + 2y)

b) 2x³ - 6x²

= 2x².(x - 2)

c) 18x² - 20xy

= 2x.(9x - 10y)

d) xy + y² - x - y

= (xy + y²) - (x + y)

= y(x + y) - (x + y)

= (x + y)(y - 1)

e) (x²y² - 8)² - 1

= (x²y² - 8 - 1)(x²y² - 8 + 1)

= (x²y² - 9)(x²y² - 7)

= (xy - 3)(xy + 3)(x²y² - 7)

f) x² - 7x - 8

= x² - 8x + x - 8

= (x² - 8x) + (x - 8)

= x(x - 8) + (x - 8)

= (x - 8)(x + 1)

a: \(3x^3+6x^2y\)

\(=3x^2\cdot x+3x^2\cdot2y=3x^2\left(x+2y\right)\)

b: \(2x^3-6x^2=2x^2\cdot x-2x^2\cdot3=2x^2\left(x-3\right)\)

c: \(18x^2-20xy=2x\cdot9x-2x\cdot10y=2x\left(9x-10y\right)\)

d: \(xy+y^2-x-y\)

\(=y\left(x+y\right)-\left(x+y\right)\)

\(=\left(x+y\right)\left(y-1\right)\)

e: \(\left(x^2y^2-8\right)^2-1\)

\(=\left(x^2y^2-8-1\right)\left(x^2y^2-8+1\right)\)

\(=\left(x^2y^2-7\right)\left(x^2y^2-9\right)\)

\(=\left(x^2y^2-7\right)\left(xy-3\right)\left(xy+3\right)\)

f: \(x^2-7x-8\)

\(=x^2-8x+x-8\)

\(=x\left(x-8\right)+\left(x-8\right)=\left(x-8\right)\left(x+1\right)\)

g: \(10x^2\left(2x-y\right)+6xy\left(y-2x\right)\)

\(=2x\cdot\left(2x-y\right)\cdot5x-2x\cdot\left(2x-y\right)\cdot3y\)

\(=2x\left(2x-y\right)\left(5x-3y\right)\)

h: \(x^2-2x+1-y^2\)

\(=\left(x-1\right)^2-y^2\)

\(=\left(x-1-y\right)\left(x-1+y\right)\)

i: \(2x\left(x+2\right)+x^2\left(-x-2\right)\)

\(=2x\left(x+2\right)-x^2\left(x+2\right)\)
\(=\left(x+2\right)\left(2x-x^2\right)=x\cdot\left(x+2\right)\left(2-x\right)\)

k: \(-x^2+6x-9=-\left(x^2-6x+9\right)\)

\(=-\left(x^2-2\cdot x\cdot3+3^2\right)=-\left(x-3\right)^2\)

l: \(-2x^2+8xy-8y^2\)

\(=-2\left(x^2-4xy+4y^2\right)\)

\(=-2\left(x-2y\right)^2\)

m: \(3x^2+5x-3y^2-5y\)

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

\(=3\left(x-y\right)\left(x+y\right)+5\left(x-y\right)\)

\(=\left(x-y\right)\left(3x+3y+5\right)\)

g) 10x²(2x - y) + 6xy(y - 2x)

= 10x²(2x - y) - 6xy(2x - y)

= 2x(2x - y)(5x - 3y)

h) x² - 2x + 1 - y²

= (x² - 2x + 1) - y²

= (x - 1)² - y²

= (x - y - 1)(x + y - 1)

i) 2x(x + 2) + x² (-x - 2)

= 2x(x + 2) - x²(x + 2)

= x(x + 2)(2 - x)

k) -9 + 6x - x²

= -(x² - 6x + 9)

= -(x - 3)²

l) 8xy - 2x² - 8y²

= -2(x² - 4xy + 4y²)

= -2(x - 2y)²

m) 3x² + 5x - 3y² - 5y

= (3x² - 3y²) + (5x - 5y)

= 3(x² - y²) + 5(x - y)

= 3(x - y)(x + y) + 5(x - y)

= (x - y)[3(x + y) + 5]

= (x - y)(3x + 3y + 5)

đề bài là rút gọn à

BÀI 1:

A) THAY X =2 ; Y= 1/3 VÀO BIỂU THỨC

2. ( 2+ 2) + 1/3. ( 1/3 + 3) + 2^2 + 2. (1/3) ^2 + 4. 1/3

= 2.4 + 1/3 . 10/3+ 4+ 2. 1/9 + 4/3

= 8+ 10/9 + 4+ 2/9 + 4/3

= 44/3

B) THAY X= 2; Y= 1/3 VÀO BIỂU THỨC

( 2 + 1/3 ) . 2 + ( 2- 1/3 ) . 2

= 7/3 . 2 + 5/3 . 2

= 7/6 + 10/3

= 9/2

C) TA CÓ: ( X+ Y) X + ( X+Y ) X= 2. X.( X+Y)

THAY X= 2; Y= 1/3 VÀO BIỂU THỨC

2. 2.( 2+ 1/3)

= 4. 7/3

= 28/3

BÀI 2:

A) \(\left(x^2+6x+5\right)+\left(-3x+9\right)=x^2+6x+5-3x+9\)

\(=\left(6x-3x\right)+\left(5+9\right)+x^2\)

\(=3x+14+x^2\)

B) \(\left(2x^2+3x+7\right)-\left(-2x+5\right)=2x^2+3x+7+2x-5\)

\(=2x^2+\left(3x+2x\right)+\left(7-5\right)\)

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

C) \(\left(6x^2y-6xy^2\right)+\left(7xy+4xy^2-x^2y\right)=6x^2y-6xy^2+7xy+4xy^2-x^2y\)

\(=\left(6x^2y-x^2y\right)+\left(4xy^2-6xy^2\right)+7xy\)

\(=5x^2y+\left(-2xy^2\right)+7xy\)

CHÚC BN HỌC TỐT!!!!
 

Chọn C

a) A = x^3 + 6x^2y + 12xy^2 + 8y^3

=> A = ( x + 2y )^3

Thay x + 2y = -5 vào A

=> A = ( -5 )^3 = -125

Vậy khi x + 2y = -5 thì A = -125

b) B = 8x^3 - 12x^2y + 6xy^2 - y^3

=> B = ( 2x - y )^3

Thay 2x - y = 1/5 vào A

=> A = ( 1/5 )^3 = 1/125

Vậy khi 2x - y = 1/5 thì B = 1/125

c) C = x^3 + 3x^2 + 3x + 1

=> C = ( x + 1 )^3

Thay x = 99 vào C

=> C = ( 99 + 1 )^3 = 100^3 = 1000000

Vậy khi x = 99 thì C = 1000000

Để tính các biểu thức trên, ta sẽ áp dụng quy tắc nhân đa thức.

a) 2xy(3x+1) = 6x^2y + 2xy

b) -6x^2y(4x-5) = -24x^3y + 30x^2y

c) -3x^2(4x^2y-6xy) = -12x^4y + 18x^3y

d) 1/2xy^2(2x+3) = xy^2 + 3/2xy^2

e) 8x^2y^2(1/4xy-1/2x^2) = 2xy - 4x^2y^2

f) 5x(x^2+3x+1) = 5x^3 + 15x^2 + 5x

g) -1/2x^2y(2xy+6) = -x^3y - 3x^2y

a,\(14x^2y-21xy=7xy.\left(2x-3\right)\)

b,\(-x^2+6x-9=-\left(x^2-6x+9\right)=-\left(x-3\right)^2\)

c,\(3x^2-6xy+3y^2-27=3.\left(x^2-2xy+y^2-9\right)=3.\text{[}\left(x-y\right)^2-3^2\text{]}=3.\left(x-y-3\right).\left(x-y+3\right)\)

a) 14x²y - 21xy

= 7xy (2x - 3)

b) -x² + 6x - 9

= -(x² - 6x + 3²)

= -(x - 3)²

c) 3x² - 6xy + 3y² - 27

= 3 (x² - 2xy + y² - 9)

= 3 [(x² - 2xy + y²) - 9]

= 3 [(x - y)² - 3²]

= 3 (x - y - 3) (x - y + 3)

#Học tốt!!!

~NTTH~

a,

$xy^2+x^2y+(-2xy^2)=xy^2-2xy^2+x^2y=-xy^2+x^2y$

b,

$12x^2y^3z^4+(-7x^2y^3z^4)=12x^2y^3z^4-7x^2y^3z^4=5x^2y^3z^4$

c,

$-6xy^3-(-6xy^3)+6x^3=-6xy^3+6xy^3+6x^3=0+6x^3=6x^3$

d,

$\frac{-x^2}{2}+\frac{7}{2}x^2+x=(\frac{7}{2}-\frac{1}{2})x^2+x$

$=3x^2+x$

e,

$2x^3+3x^3-\frac{1}{3}x^3=(2+3-\frac{1}{3})x^3=\frac{14}{3}x^3$

f,

$5xy^2+\frac{1}{2}xy^2+\frac{1}{4}xy^2=(5+\frac{1}{2}+\frac{1}{4})xy^2$

$=\frac{23}{4}xy^2$