\(=4x^2-4xy-13xy+13y^2=4x\left(x-y\right)-13y\left(x-y\right)=\left(4x-13y\right)\left(x-y\right)\)

\(4x^2-17xy+13y^2=\left(4x^2-4xy\right)+\left(13y^2-13xy\right)=4x\left(x-y\right)+13y\left(x-y\right)=\left(4x+13y\right)\left(x-y\right)\)

\(4x^2-17xy+13y^2\\ =4x^2-4xy-13xy+13y^2\\ =4x\left(x-y\right)-13y\left(x-y\right) \\ =\left(x-y\right)\left(4x-13y\right)\)

a,\(x^2-y^2+2x+1=\left(x^2-2x+1\right)-y^2=\left(x+1\right)^2-y^2=\left(x+1-y\right)\left(x+1+y\right)\)b

\(4x^2-17xy+13y^2=\left(4x^2-4xy\right)+\left(13y^2-13xy\right)=4x\left(x-y\right)-13y\left(x-y\right)\)\(=\left(4x-13y\right)\left(x-y\right)\)

Nếu thấy đúng thì tick nha bạn,cảm ơn.

a) 4x² - 17xy + 13y²

=4x²-4xy-13xy+13y²

=4x(x-y)-13y(x-y)

=(x-y)(4x-13y)

b) x⁸ + x⁴ +1

=x⁸+2x⁴+1-x⁴

=(x⁴+1)²-x⁴

=(x⁴+1-x²)(x⁴+1+x²)

\(x^8+x^4+1\)

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

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

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

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

4x²-17xy+13y²

=4x²-4xy-13xy+13y²

=4x(x-y)-13y(x-y)

=(x-y)(4x-13y)

\(4x^2-17xy+13y^2\)

\(=4x^2-4xy-13xy+13y^2\)

\(=4x\left(x-y\right)-13y\left(x-y\right)\)

\(=\left(x-y\right)\left(4x-13y\right)\)

Giải:

\(4x^2-17xy+13y^2\)

\(=4x^2-8xy+4y^2+9y^2-9xy\)

\(=4\left(x^2-2xy+y^2\right)+9y^2-9xy\)

\(=4\left(x-y\right)^2+9y\left(y-x\right)\)

\(=4\left(y-x\right)^2+9y\left(y-x\right)\)

\(=\left(y-x\right)\left[4\left(y-x\right)+9y\right]\)

\(=\left(y-x\right)\left(4y-4x+9y\right)\)

\(=\left(y-x\right)\left(13y-4x\right)\)

Vậy ...

\(a,=\left(3-x+1\right)\left(9+3x-3+x^2-2x+1\right)\\ =\left(4-x\right)\left(x^2+x+7\right)\\ b,=4x^2-4xy-13xy+13y^2\\ =4x\left(x-y\right)-13y\left(x-y\right)\\ =\left(4x-13y\right)\left(x-y\right)\\ c,=4\left(x^2-xy-2y^2\right)\\ =4\left(x^2+xy-2xy-2y^2\right)\\ =4\left(x+y\right)\left(x-2y\right)\\ d,=x^3+4x^2+5x^2+20x+6x+24\\ =\left(x+4\right)\left(x^2+5x+6\right)\\ =\left(x+4\right)\left(x^2+2x+3x+6\right)\\ =\left(x+4\right)\left(x+2\right)\left(x+3\right)\\ f,=x\left(x+4y\right)-3\left(x+4y\right)=\left(x-3\right)\left(x+4y\right)\\ g,=4x^3+4x^2-29x^2-29x-24x-24\\ =\left(x+1\right)\left(4x^2-29x-24\right)\\ =\left(x+1\right)\left(4x^2-32x+3x-24\right)\\ =\left(x+1\right)\left(x-8\right)\left(4x+3\right)\)

\(a,27-\left(x-1\right)^3=\left(3-x+1\right)\left[9+3\left(x-1\right)+\left(x+1\right)^2\right]=\left(4-x\right)\left(9+3x-3+x^2+2x+1\right)=\left(4-x\right)\left(x^2+5x+7\right)\)

\(b,4x^2-17xy+13y^2=\left(4x^2-4xy\right)-\left(13xy-13y^2\right)=4x\left(x-y\right)-13y\left(x-y\right)=\left(x-y\right)\left(4x-13y\right)\)

\(c,4x^2-4xy-8y^2=4\left(x^2-xy-2y^2\right)\)

\(d,x^3+9x^2+26x+24=\left(x^3+2x^2\right)+\left(7x^2+14x\right)+\left(12x+24\right)=\left(x+2\right)\left(x^2+7x+12\right)=\left(x+2\right)\left[\left(x^2+3x\right)+\left(4x+12\right)\right]=\left(x+2\right)\left(x+3\right)\left(x+4\right)\)

\(f,4xy+x^2-3x-12y=x\left(4y+x\right)-3\left(x+4y\right)=\left(x+4y\right)\left(x-3\right)\)

\(g,4x^3-25x^2-53x-24=\left(4x^3-32x^2\right)+\left(7x^2-56x\right)+\left(3x-24\right)=\left(4x^2+7x+3\right)\left(x-8\right)=\left[\left(4x^2+4x\right)+\left(3x+3\right)\right]=\left(4x+3\right)\left(x+1\right)\left(x-8\right)\)

A - B = ( 5x² - 12xy + 2y² ) + ( -4x² + 12xy - y² )

        = 5x² - 12xy + 2y²  -  4x² + 12xy - y²

           = 9x² + y²

        x² > hoặc = 0 => 9x² > hoặc = 0

      y² > hoặc = 0

<=> 9x² + y² > hoặc = 0

A + B > hoặc = 0

nên A và B không cùng có giá trị âm

tương tự 2) lấy A - B 

              3) lấy A + B