\(5x^4y+10x^3y+10x^2y^3+5xy^4\)

\(=5xy.x^3+5xy.2x^3+5xy.2xy^3+5xy.y^3\)

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

Ht pt

đúng ,mình k 2 nhé

x²-2xy+y²+3x-3y-10

= (x-y)²+3(x-y)-10

= [(x-y)²+5(x-y)]-[2(x-y)+10]

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

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

Ta có: \(x^2-2xy+y^2+3x-3y-10\)

\(=\left(x-y\right)^2+3\left(x-y\right)-10\)

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

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

\(3x^3+6x+3-3y^2=3\left[\left(x^2+2x+1\right)-y^2\right]=3\left[\left(x+1\right)^2-y^2\right]=3\left(x-y+1\right)\left(x+y+1\right)\)

\(5x^2-4\left(x^2-2x+1\right)-5=\left(5x^2-5\right)-4\left(x-1\right)^2=5\left(x^2-1\right)-4\left(x-1\right)^2=5\left(x-1\right)\left(x+1\right)-4\left(x-1\right)^2=\left(x-1\right)\left[5\left(x+1\right)-4\left(x-1\right)\right]=\left(x-1\right)\left(5x+5-4x+4\right)=\left(x-1\right)\left(x+9\right)\)

\(= \)\(5x^2-4x^2+8x-4-5\)

\(=\)\(x^2+8x-9\)

\(=x^2+9x-x-9\)

\(=(x-1)(x+9)\)

\(5x^2-4\left(x^2-2x+1\right)-5\)

\(=5x^2-4x^2+8x-4-5\)

\(=x^2+8x-9\)

\(=\left(x+9\right)\left(x-1\right)\)

a) x²+x-2
= x²-x+2x-2
= x(x-1)+2(x-1)
= (x+2)(x-1)
b) 2x²+5x+3
= 2x²+2x+3x+3
= 2x(x+1)+3(x+1)
= (2x+3)(x+1)
c) 3x²+5x-2
= 3x²+6x-1x-2
= 3x(x+2)-1(x+2)
= (3x-1)(x+2)

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

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

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

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

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

2) \(3x+3y-x^2-2xy-y^2\)

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

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

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

3) \(x^4-x\)

\(=x\left(x^3-1\right)\)

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

4) \(x^2+5x+4\)

\(=x^2+x+4x+4\)

\(=x\left(x+1\right)+4\left(x+1\right)\)

\(=\left(x+1\right)\left(x+4\right)\)

5) \(4x^2+4x-8\)

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

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

\(=4\left[x\left(x-1\right)+2\left(x-1\right)\right]\)

\(=4\left(x-1\right)\left(x+2\right)\)

6) \(x^2+x-42\)

\(=x^2-6x+7x-42\)

\(=x\left(x-6\right)+7\left(x-6\right)\)

\(=\left(x-6\right)\left(x+7\right)\)

7) \(5x^2-3x-2\)

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

\(=5x\left(x-1\right)+2\left(x-1\right)\)

\(=\left(x-1\right)\left(5x+2\right)\)

8) \(x^2-4x-1\)

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

\(=\left(x-2\right)^2-5\)

\(=\left(x-2+\sqrt{5}\right)\left(x-2-\sqrt{5}\right)\)

9) \(x^2-7xy+12y^2\)

\(=x^2-3xy-4xy+12y^2\)

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

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

Ta có: \(\left(4x+1\right)\left(12x-1\right)\left(3x+2\right)\left(x+1\right)-4\)

\(=\left(12x^2+8x+3x+2\right)\left(12x^2+12x-x-1\right)-4\)

\(=\left(12x^2+11x+2\right)\left(12x^2+11x-1\right)-4\)

\(=\left(12x^2+11x\right)^2+\left(12x^2+11x\right)-6\)

\(=\left(12x^2+11x+3\right)\left(12x^2+11x-2\right)\)

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

b: \(=2x^2+10x-3x-15\)

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