\(5x^2-30x-20y^2+45\)

\(=5\left(x^2-6x-4y^2+9\right)\)

\(=5\left[\left(x-3\right)^2-4y^2\right]\)

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

Ta có: 

a) 5x - 20y = 5(x - 4y)

b) 5x(x - 1) - 3x(x - 1) = x(x - 1)2

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

d) x² - 9 = (x - 3)(x + 3)

e) 4² - 25 = (4 - 5)(4 + 5) f) x⁶ - y⁶ = (x⁴)² - (y⁴)² = (x⁴ - y⁴)(x⁴ + y⁴) 

a)  5x - 20y = 5( x - 4y)

b) 5x(x-1) - 3x(x-1) =2x (x-1) 

c) x² - 9 = x² - 3² = ( x-3)(x+3)

e) 4²-25 = 4² - 5² = ( 4-5)(4+5)= -9

f) x⁶ - y⁶ = (x³)² - (y³)² = ( x³ - y³ ) ( x³ + y³)

                                    = (x-y) ( x² + xy + y² ) ( x+y) ( x² -xy +y²)

mình làm thiếu câu c ) x(x+y) - 5x-5y 

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

                                    = (x+y) ( x-5)

12

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

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

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

2) Câu b sai đề nên mk sửa lại nha

2x³ + x² - 8x - 4

= (2x³ + x²) - (8x + 4)

= x².(2x + 1) - 4.(2x + 1)

= (2x + 1).(x² - 4)

= (2x + 1).(x - 2).(x + 2)

3) 2x² - 8xy - 5x + 20y

= (2x² - 5x) - (8xy - 20y)

= x.(2x - 5) - 4y.(2x - 5)

= (2x - 5).(x - 4y)

1) ( x+1) ( x-y)

2) 2x³ + x² - 8x - 4= 2x³ - 4x² + 5x² - 10x + 2x - 4 = 2x² ( x-2) + 5x( x -2) + 2(x -2)

=( 2x² + 5x + 2)( x-2)

=( 2x² + 4x + x + 2)( x-2)

=[ 2x( x+2) + ( x-2)]( x-2)

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

3) 2x² - 8xy - 5x + 20y

= 2x ( x - 4y) - 5( x-4y)= ( 2x-5)(x-4y)

1/

a)5x – 20y=5(x-4y)

b) 5x.(x –  1) –  3x(x – 1)=2x(x-1)

c) x.(x+y) – 5x – 5y=c) x.(x+y) – 5(x+y)=(x-5)(x+y)

2/

a)x² + xy + x = x(x+y+1)=77.(77+22+1)=77.100=7700

b)  x . ( x – y ) + y . ( y – x )=(x-y)(x-y)=(x-y)²=(53-3)²=2500

3/

a) X + 5x² = 0

⇒x(x+5)=0

⇒hoặc x=0

x+5=0⇒x=-5

b)x + 1 = ( x + 1 )² 

⇒(x + 1)-( x + 1 )² =0

⇒x(x+1)=0

⇒ hoặc x=0

hoặc x+1=0⇒x=-1

4/

a) 97 . 13 + 130 . 0,3 = 97.13+13.10.0,3=97.13+13.3=100.13=1300

b)86 . 153 – 530 . 8,6=86.153–53.10.8,6=86.153-53.86=86.100=8600

C) 85 .12,7 + 5,3 . 12,7= 12,7(85+5,3)=12,7.90,3=1146,81

D)52.143 – 52 . 39 – 8.26=52(143-39)-8,26=52.104-8,26=5399,74

Bài 1:  

a) 5x-20y=5(x-4y)

b) \(5x\left(x-1\right)-3x\left(x-1\right)=2x\left(x-1\right)\)

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

Bài 2: 

a) \(x^2+xy+x\)

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

\(=77\cdot\left(77+22+1\right)\)

=7700

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

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

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

\(=50^2=2500\)

Gọi P là biểu thức phải phân tích, ta có 
P = a(b + c)^2(b - c) + b(c + a)^2(c - a) - c(a + b)^2[(b - c) + (c - a)] 
= a(b + c)^2(b - c) + b(c + a)^2(c - a) - c(a + b)^2(b - c) - c(a + b)^2(c - a) 
= [a(b + c)^2(b - c) - c(a + b)^2(b - c)]+ [b(c + a)^2(c - a) - c(a + b)^2(c - a)] 
= (b - c)[a(b + c)^2 - c(a + b)^2] + (c - a)[b(c + a)^2 - c(a + b)^2] 
= (b - c)(ab^2 + ac^2 - ca^2 - cb^2) + (c - a)(bc^2 + ba^2 - ca^2 - cb^2) 
= (b - c)[ac(c - a) - b^2(c - a)] + (c - a)[a^2(b - c) - bc(b - c)] 
= (b - c)(c - a)(ac - b^2) + (c - a)(b - c)(a^2 - bc) 
= (b - c)(c - a)(ac - b^2 + a^2 - bc) 
= (b - c)(c - a)[(a^2 - b^2) + (ac - bc)] 
= (b - c)(c - a)[(a - b)(a + b) + c(a - b)] 
= (b - c)(c - a)(a - b)(a + b + c) 
= (a - b)(b - c)(c - a)(a + b + c). 
Vậy P = (a - b)(b - c)(c - a)(a + b + c).

\(5y^3-10xy^2+5yx^2-20y=5y\left(y^2-2xy+x^2-4\right)\)

                                                              \(=5y\left[\left(x+y\right)^2-4\right]\)

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

Chúc bạn học tốt.