\(1,\\ 1,=15\left(x+y\right)\\ 2,=4\left(2x-3y\right)\\ 3,=x\left(y-1\right)\\ 4,=2x\left(2x-3\right)\\ 2,\\ 1,=\left(x+y\right)\left(2-5a\right)\\ 2,=\left(x-5\right)\left(a^2-3\right)\\ 3,=\left(a-b\right)\left(4x+6xy\right)=2x\left(2+3y\right)\left(a-b\right)\\ 4,=\left(x-1\right)\left(3x+5\right)\\ 3,\\ A=13\left(87+12+1\right)=13\cdot100=1300\\ B=\left(x-3\right)\left(2x+y\right)=\left(13-3\right)\left(26+4\right)=10\cdot30=300\\ 4,\\ 1,\Rightarrow\left(x-5\right)\left(x-2\right)=0\Rightarrow\left[{}\begin{matrix}x=2\\x=5\end{matrix}\right.\\ 2,\Rightarrow\left(x-7\right)\left(x+2\right)=0\Rightarrow\left[{}\begin{matrix}x=7\\x=-2\end{matrix}\right.\\ 3,\Rightarrow\left(3x-1\right)\left(x-4\right)=0\Rightarrow\left[{}\begin{matrix}x=\dfrac{1}{3}\\x=4\end{matrix}\right.\\ 4,\Rightarrow\left(2x+3\right)\left(2x-1\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=-\dfrac{3}{2}\\x=\dfrac{1}{2}\end{matrix}\right.\)

P(x)=x(x+3)(x+1)(x+2)+1

P(x)=(x²+3x)(x²+3x+2)+1

Đặt x²+3x=a

Ta có:

P(x)=a(a+2)+1

P(x)=a²+2a+1

P(x)=(a+1)²

Vậy P(x)=(x²+3x)²

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

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

x(x - y) - 2(y -x) = (x - 2)(y - x)

1/ = x⁴ + 2x³ + 4x² + 3x - 10 = (x⁴ - x³) + (3x³ - 3x²) + (7x² - 7x) + (10x - 10)

= (x - 1)(x³ + 3x² + 7x + 10) = (x - 1)[(x³ + 2x²) + (x² + 2x) + (5x + 10)]

= (x - 1)(x + 2)(x² + x + 5)

2/ = (x⁵ - 2x⁴) + (x⁴ - 2x³) + (x³ - 2x²) + (x² - 2x) + (x - 2) = (x - 2)(x⁴ + x³ + x² + x + 1)

a) x³-2x²-x+2

=x(x²-1)+2(-x²+1)

=x(x²-1)-2(x²-1)

=(x²-1)(x-2)

b)

x²+6x-y²+9

=x²+6x+9-y²

=(x+3)²-y²

^{=(x+3-y)(x+3+y)}

8x³ - 27y³ = 2³ . x³ - 3³ . y³ = ( 2x )³ - ( 3y )³ = ( 2x - 3y ) [(2x)² + 12xy + (3y)² ]. 

\(33\left(x-1\right)2y^2-11\left(1-x\right)y^3\)

\(=33\left(x-1\right)2y^2+11\left(x-1\right)y^3\)

\(=\left(x-1\right)\left[66y^2+11y^3\right]\)

\(=11y^2\left(x-1\right)\left[6+y\right]\)

`a)5(x-y)-y(x-y)`

`=(x-y)(5-y)`

`b)x^2-6x-y^2+9`

`=(x^2-6x+9)-y^2`

`=(x-3)^2-y^2`

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

1

(x²-8)²+36

=x⁴-16x²+64+36

=x⁴+20x²+100-36x²

=(x²+10)²-(6x)²

HĐT số 3

3

(a+c+b)³-a³-b³-c³

=a³+b³+c³+3(a+b)(a+c)(b+c)-a³-b³-c³

^{=3(a+b)(a+c)(c+b)}