\(5x^2y-xy=xy\left(5x-1\right)\)

\(5 x 2 y − x y = x y ( 5 x − 1 )\)

5x2y - xy = xy (5x - 1)

\(a,5x^2y-10xy^2=5xy\left(x-2y\right)\\ b,x^2+2xy+y^2-5x-5y=\left(x+y\right)^2-5\left(x+y\right)=\left(x+y\right)\left(x+y-5\right)\\ c,x^2-6x+8=\left(x^2-2x\right)-\left(4x-8\right)=x\left(x-2\right)-4\left(x-2\right)=\left(x-2\right)\left(x-4\right)\\ d,5x^2-10xy+5y^2-20z^2=5\left(x^2-2xy+y^2-4z^2\right)=5\left[\left(x-y\right)^2-\left(2z\right)^2\right]=5\left(x-y-2z\right)\left(x-y+2z\right)\)

\(a,=\left(x-y\right)\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(x-y-1\right)\\ b,=\left(x+y\right)\left(x-5\right)\\ c,=5x^2\left(x-y\right)-10x\left(x-y\right)=5x\left(x-2y\right)\left(x-y\right)\\ d,=x^2-2xy=x\left(x-2y\right)\\ e,=\left(3x-2y\right)\left(9x^2+6xy+4y^2\right)\)

a, Thay x = -2 và  y = 1 vào BT, ta được:

\(M=5.\left(-2\right)^2.1+3.\left(-2\right).1-21=20-6-21=-7\)

b, Ta có: \(a^2-a-6=a^2-3a+2a-6=a\left(a-3\right)+2\left(a-3\right)=\left(a-3\right)\left(a+2\right)\)

a) Thay x=-2 và y=1 vào M, ta được:

\(M=5\cdot\left(-2\right)^2\cdot1+3\cdot\left(-2\right)\cdot1-21\)

\(=5\cdot4-3\cdot2-21\)

\(=20-6-21=14-21=-7\)

b) Ta có: \(a^2-a-6\)

\(=a^2-3a+2a-6\)

\(=a\left(a-3\right)+2\left(a-3\right)\)

\(=\left(a-3\right)\left(a+2\right)\)

\(5x^2y+5xy^2-a^2x-a^2y\)

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

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

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

b) \(3x^3+6x^2+3x=3x\left(x^2+2x+1\right)=3x\left(x+1\right)^2\)

c) \(3x^2y-12y=3y\left(x^2-4\right)=3y\left(x-2\right)\left(x+2\right)\)

d) \(7x^3-28x^2+28x=7x\left(x^2-4x+4\right)=7x\left(x-2\right)^2\)

a: \(5x^2y-20xy+20y\)

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

\(=4x\left(x-2\right)^2\)

b: \(3x^3+6x^2+3x\)

\(=3x\left(x^2+2x+1\right)\)

\(=3x\left(x+1\right)^2\)

c: \(3x^2y-12y\)

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

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

d: \(7x^3-28x^2+28x\)

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

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

a) 8 - 27x³

= (2 - 3x) (4 + 6x + 9x²)

b) 5x²y - 10xy - 5y²

= 5y(x² - 2x - y)

c) x³ + 8y³

= (x + 2y) (x² - 2xy + 4y²)

d) 3x² + 5y - 3xy - 5x

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

Bạn cần viết đề bằng công thức toán để được hỗ trợ tốt hơn.

a, 2xy^2 ( x^3 -3xy - 4 )

b, x^2 - 4x - 4x +16

= x(x-4) - 4(x-4)

= (x-4) (x-4)

Lời giải:

a.

$2x^4y^2-6x^2y^3-8xy^2=2xy^2(x^3-3xy-4)$

b. 

$x^2-8x+16=x^2-2.4.x+4^2=(x-4)^2$

c.

$12x^2-12=12(x^2-1)=12(x-1)(x+1)$

d. 

$5x^2y-20xy+20y=5y(x^2-4x+4)=5y(x-2)^2$
e.

$3x^2y^2-27y^2=3y^2(x^2-9)=3y^2(x-3)(x+3)$

f. 

$8x^3-27y^3=(2x)^3-(3y)^3=(2x-3y)(4x^2+6xy+9y^2)$

g.

$4x^4-8x^3+4x^2=(2x^2)^2-2.2x^2.2x+(2x)^2$

$=(2x^2-2x)^2=[2x(x-1)]^2=4x^2(x-1)^2$
h.

$7x^2y^2-28y^4=7y^2(x^2-4y^2)=7y^2(x-2y)(x+2y)$

$

Ta có: \(A+B+C=0\)

\(\Leftrightarrow3x^2y+5xy^2-2xy+1+2x^2y-7xy^2+6xy-8-5x^2y+4xy^2-4xy+12=0\)

\(\Leftrightarrow2xy^2+5=0\)

\(\Leftrightarrow2x\cdot\left(-2\right)^2+5=0\)

\(\Leftrightarrow8x+5=0\)

\(\Leftrightarrow8x=-5\)

hay \(x=-\dfrac{5}{8}\)

Vậy: \(x=-\dfrac{5}{8}\)