\(a,\)\(x^3-13x-12\)

\(=x^3-x-12x-12\)

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

\(=x\left(x-1\right)\left(x+1\right)-12\left(x+1\right)\)

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

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

\(=\left(x+1\right)\left[x\left(x-4\right)+3\left(x+4\right)\right]\)

\(=\left(x+1\right)\left(x-4\right)\left(x+3\right)\)

a) \(x^3-13x-12\)

\(=x^3+x^2-x^2-x-12x-12\)

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

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

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

\(=\left(x+1\right)\left[x\left(x-4\right)+3\left(x-4\right)\right]\)

\(=\left(x+1\right)\left(x-4\right)\left(x+3\right)\)

b) \(2x^4+3x^3-9x^2-3x+2\)câu này hình như sai đề rồi, bạn xem lại nhen

c) \(x^4-3x^3-6x^2+3x+1\)câu này cx thế, bạn xem lại nha

b) \(2x^4+3x^3-9x^2-3x+2\)

\(=\left(2x^4-2x^3-2x^2\right)+\left(5x^3-5x^2-5x\right)-\left(2x^2-2x-2\right)\)

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

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

\(\left(ab-1\right)^2+\left(a+b\right)^2=a^2b^2-2ab+1+a^2+2ab+b^2=a^2+b^2+a^2b^2+1=a^2\left(b^2+1\right)+\left(b^2+1\right)=\left(a^2+1\right)\left(b^2+1\right)\)

\(\left(ab-1\right)^2+\left(a+b\right)^2=a^2b^2-2ab+1+a^2+2ab+b^2=a^2b^2+a^2+b^2+1=\left(a^2b^2+a^2\right)+\left(b^2+1\right)=a^2\left(b^2+1\right)+\left(b^2+1\right)=\left(a^2+1\right)\left(b^2+1\right)\)

\(\left(ab-1\right)^2+\left(a+b\right)^2\)

\(=a^2b^2+1+a^2+b^2\)

\(=\left(a^2+1\right)\left(b^2+1\right)\)

a. 3x - 3 + 5(x - 1)

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

= (3 + 5)(x - 1)

= 8(x - 1)

b. x² - 25 + y² - 2xy

= (x² - 2xy + y²) - 25

= (x - y)² - 5²

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

c. x² + 2xy - 16a² + y²

= (x² + 2xy + y²) - 16a²

= (x + y)² - (4a)²

= (x + y + 4a)(x + y - 4a)

\(a,Sửa:x^2-xy-13x+13y=x\left(x-y\right)-13\left(x-y\right)=\left(x-13\right)\left(x-y\right)\\ b,=\left(x+y\right)^2-\left(2z\right)^2=\left(x+y-2z\right)\left(x+y+2z\right)\\ c,=\left(x^2-2x\right)-\left(3x-6\right)=x\left(x-2\right)-3\left(x-2\right)=\left(x-2\right)\left(x-3\right)\)

B1 :

a, B = (x+1)^2+(y-2)^2 = (99+1)^2+(102-2)^2 =  100^2+100^2 = 20000

b, = (2x^2+16x+32)-2y^2

   = 2.(x+4)^2-2y^2

   = 2.[(x+4)^2-y^2] = 2.(x+4-y).(x+4+y)

c, <=> (x^2-3x)+(2x-6) = 0

<=> (x-3).(x+2) = 0

<=> x-3=0 hoặc x+2=0

<=> x=3 hoặc x=-2

B2 :

P = (3-x).(x+3)/x.(x-3) = -(x+3)/x = -x-3/x

k mk nha

Bai 1

a)B=(x+1)²+(y-2)²

     Voi x=99,y=102

=>B= 100²+100²

       =20000

b)\(2x^2-2y^2+16x+32\)

=\(2\left[\left(x^2+8x+16\right)-y^2\right]\)

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

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

c)\(x^2-3x+2x-6=0\)

=>x(x-3)+2(x-3)=0

=>(x-3)(x+2)=0

=>x=-2;3

Bai 2

\(P=\frac{9-x^2}{x^2-3x}\)

    =\(-\frac{x^2-9}{x\left(x-3\right)}\)

   =\(-\frac{\left(x-3\right)\left(x+3\right)}{x\left(x-3\right)}\)

=\(\frac{-x-3}{x}\)

bafi 1: a) \(B=x^2+2x+1+y^2-4y+4\)

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

khi \(x=99\); \(y=102\)ta co:

\(B=\left(99+1\right)^2+\left(102-2\right)^2\)

\(B=100^2+100^2\)

\(B=10000+10000\)

\(B=20000\)

c) \(x^2-3x+2x-6=0\)

\(x\left(x-3\right)+2\left(x-3\right)=0\)

\(\left(x+2\right)\left(x-3\right)=0\)

\(\Rightarrow\orbr{\begin{cases}x+2=0\\x-3=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=-2\\x=3\end{cases}}\)

vay \(\orbr{\begin{cases}x=-2\\x=3\end{cases}}\)

bai 2:

\(P=\frac{9-x^2}{x^2-3x}\)

\(P=\frac{\left(3-x\right)\left(x+3\right)}{x\left(x-3\right)}\)

\(P=\frac{-\left(x+3\right)}{x}\)\(\left(x\ne0\right)\)

\(P=\frac{-x-3}{x}\)

vay \(P=\frac{-x-3}{x}\)

a, a²+b²+2ab+2a+2b+1=(a+b+1)²

b,3x(x-2y)+6y(2y-x)=3x(x-2y)-6y(x-2y)

=3(x-2y)(x-2y)=3(x-2y)²

c, 16xy +4y²-9 +16x²=(16x²+16xy+4y²)-3²

=(4x-2y)²-3²=(4x-2y+3)(4x-2y-3)

a: \(x^4+3x^3+x^2+3x\)

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

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

c: \(x^2-xy-x+y\)

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

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