\(=6x^2+5x-3xy\)

\(=x\left(6x+5-3y\right)\)

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

x(x-4)+5(x-4)

(x+5)(x-4)

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

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

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

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

Ta có

a,    x²-x-y²-y

=x²-y²-(x+y)

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

=(x+y)(x-y-1)

b,   x²-2xy+y²-z²

=(x-y)²-z²

=(x-y-z)(x-y+z)

con bai 32, 33 neu ban tra loi duoc minh h them

nhanh nha

\(x^3-64=x^3-4^3\)

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

x³-64=x³-4³=(x-4)(x²+4x+16)

Ta có:\(x^3-64\)

\(=x^3-4^3\)

Áp dụng hằng đẳng thức:\(a^3-b^3=\left(a-b\right)\left(a^2+ab+b^2\right)\)

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

x^2 + 7x -15

= x^2 + 7x +12,25  -27,25

= (x+3,5)^2 - 27, 25

= ( x+3,5 - \(\sqrt{27,25}\))(x+3,5+\(\sqrt{27,25}\))

x^5+x+1

=x(x^4+1)+1 

=(x^2+x+1)(x^3-x^2+1) 

Ta có : x⁵ + x + 1 

= x⁵ + x⁴ - x⁴ - x³ + x³ + x² - x² - x + x + 1

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

= x⁵(x + 1) - x⁴.(x + 1) + x³(x + 1) - x²(x + 1) + (x + 1)

= (x + 1)(x⁵ - x⁴ + x³ - x² + 1)

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

\(x^2-2xy+y^2-z^2\\=(x^2-2xy+y^2)-z^2\\=(x-y)^2-z^2\\=(x-y-z)(x-y+z)\)