\(\dfrac{1}{2}\left(6x-2y\right)\left(3x+y\right)=\dfrac{1}{2}.2\left(3x-y\right)\left(3x+y\right)=9x^2-y^2\)

\(\left(\dfrac{2}{3}z-\dfrac{2}{5}x\right)\left(\dfrac{1}{3}z+\dfrac{1}{5}x\right).\dfrac{1}{2}=\left(\dfrac{1}{3}z-\dfrac{1}{5}x\right)\left(\dfrac{1}{3}z+\dfrac{1}{5}z\right).2.\dfrac{1}{2}=\dfrac{1}{9}z^2-\dfrac{1}{25}x^2\)

\(\left(5y-3x\right).\dfrac{1}{4}\left(12x+20y\right)=\left(5y-3x\right)\left(5y+3x\right).4.\dfrac{1}{4}=25y^2-9x^2\)

\(\left(\dfrac{3}{4}y-\dfrac{1}{2}x\right)\left(x+\dfrac{3}{2}y\right)=\left(\dfrac{3}{2}y-x\right)\left(\dfrac{3}{2}y+x\right)=\dfrac{9}{4}y^2-x^2\)

\(\left(a+b+c\right)\left(a+b+c\right)=\left(a+b+c\right)^2=a^2+b^2+c^2+2ab+2bc+2ac\)

\(\left(x-y+z\right)\left(x+y-z\right)=x^2-\left(y-z\right)^2=x^2-y^2-z^2+2yz\)

a: \(\dfrac{1}{2}\left(6x-2y\right)\left(3x+y\right)=\left(3x-y\right)\cdot\left(3x+y\right)=9x^2-y^2\)

b: \(\left(\dfrac{2}{3}z-\dfrac{2}{5}x\right)\left(\dfrac{1}{3}z+\dfrac{1}{5}x\right)\cdot\dfrac{1}{2}\)

\(=\left(\dfrac{1}{3}z-\dfrac{1}{5}x\right)\left(\dfrac{1}{3}z+\dfrac{1}{5}x\right)\)

\(=\dfrac{1}{9}z^2-\dfrac{1}{25}x^2\)

c: \(\left(5y-3x\right)\cdot\dfrac{1}{4}\cdot\left(12x+20y\right)\)

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

\(=25y^2-9x^2\)

d: \(\left(\dfrac{3}{4}y-\dfrac{1}{2}x\right)\left(\dfrac{3}{2}y+x\right)\cdot2\)

\(=\left(\dfrac{3}{2}y-x\right)\left(\dfrac{3}{2}y+x\right)\)

\(=\dfrac{9}{4}y^2-x^2\)

e: \(\left(a+b+c\right)\left(a+b-c\right)\)

\(=\left(a+b\right)^2-c^2\)

\(=a^2+2ab+b^2-c^2\)

a) \(5x-20y\)

\(=5\left(x-4y\right)\)

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

\(=2x\left(x-1\right)\) 

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

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

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

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)

a)5x-20y

=5x-4*5y

=5(x-4y)

b)x(x-1)-3x(x-1)

=(x-3x)(x-1)

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

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

=(x-5)(x+y)

5.(x-4)

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

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

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

\(=50^2=2500\)

a: \(5x-20y=5\left(x-4y\right)\)

b: \(x^2+x^2y+x^2y^2=x^2\left(1+y+y^2\right)\)

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

d: \(5\left(x-y\right)+y\left(x-y\right)=\left(x-y\right)\left(y+5\right)\)

a) \(5x-20y\\ =5\left(x-4y\right)\)

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

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

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

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

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

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

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

=(x+y)(x-5)

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

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

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

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