Bài 1:

$5x+10=5(x+2)$

Bài 2:

Tại $x=8$ thì $x^2+4x+4=(x+2)^2=(8+2)^2=10^2=100$

Bài 3:

$x^2-6x+9=x^2-2.3.x+3^2=(x-3)^2$

Bài 4:

Diện tích mảnh đất là:

$(x+5)(x-5)=24$

$\Leftrightarrow x^2-25=24$

$\Leftrightarrow x^2=49$

$\Rightarrow x=7$ (do $x>5$)

Chiều dài mảnh đất là: $x+5=7+5=12$ (m)

x^m+3+1+x^m+3-(x+1)=x^m+3x+x^m+3-(x+1)=x^m+3(x+1)-(x+1)=(x+1)(x^m+3-1)

 Ta có : x^m+4 + x^m+3,-x-1

<=>x^m. x⁴ + x^m . x³ - (x+1)

<=> x^m+3. (x+1) -( x+1)

<=> (x^m+3-1)(x+1)

M = x⁹ - x⁷ + x⁶ - x⁵ - x⁴ + x³ - x² + 1

= ( x⁹ - x⁷ ) + ( x⁶ - x⁴ ) - ( x⁵ - x³ ) - ( x² - 1 )

= x⁷( x² - 1 ) + x⁴( x² - 1 ) - x³( x² - 1 ) - ( x² - 1 )

= ( x² - 1 )( x⁷ + x⁴ - x³ - 1 )

= ( x - 1 )( x + 1 )[ x⁴( x³ + 1 ) - ( x³ + 1 ) ]

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

= ( x - 1 )( x + 1 )( x + 1 )( x² - x + 1 )( x² - 1 )( x² + 1 )

= ( x + 1 )²( x - 1 )( x² - x + 1 )( x - 1 )( x + 1 )( x² + 1 )

= ( x + 1 )³( x - 1 )²( x² + 1 )( x² - x + 1 )

\(x^2-y^2+4x+4\)

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

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

\(4x^2-y^2+8\left(y-2\right)\)

\(=4x^2-\left(y^2-8y+16\right)\)

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

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

\(=m^2-\left(n-2\right)^2=\left(m-n+2\right)\left(m+n-2\right)\)

(x^m+2)+(x^m) = 2x^m+2 = 2(x^m+1)

(x^x+1)-(x^x)-1 = x^x+1-x^x-1 = 0

(m^4)-(n^4) = (m²)²-(n²)² = (m²-n²)(m²+n²)

\(m^6+n^4=\left(m^3\right)^2+2.m^3.n^2+\left(n^2\right)^2-2m^3n^2\)

\(=\left(m^3+n^2\right)^2-\left(\sqrt{2m^3}n\right)^2\)

\(=\left(m^3+n^2-\sqrt{2m^3}n\right)\left(m^3+n^2+\sqrt{2m^3}n\right)\).