a) \(x^2-y^2+4y-4\)
\(=x^2-\left(y^2-4y^2+4\right)\)
\(=x^2-\left(y-2\right)^2\)
\(=\left(x-y+2\right)\left(x+y-2\right)\)
b) \(8x^3-1=\left(2x\right)^3-1^3\)\(=\left(2x-1\right)\left(4x^2+2x+1\right)\)
a)\(x^2-y^2+4y-4=x^2-\left(y-2\right)^2=\left(x+y-2\right)\left(x-y+2\right)\)
b)\(8x^3-1=\left(2x-1\right)\left(4x^2+4x+1\right)=\left(2x-1\right)\left(4x^2+2x+2x+1\right)=\left(2x-1\right)\left[2x\left(2x+1\right)+\left(2x+1\right)\right]=\left(2x-1\right)\left(2x+1\right)^2\)
c)\(x^2-x-42=x^2+6x-7x-42=x\left(x+6\right)-7\left(x+6\right)=\left(x-7\right)\left(x+6\right)\)
d)\(x^2-4x-5=x^2+x-5x-5=x\left(x+1\right)-5\left(x+1\right)=\left(x-5\right)\left(x+1\right)\)
e)\(6x^2-x-5=6x^2-6x+5x-5=6x\left(x-1\right)+5\left(x-1\right)=\left(6x+5\right)\left(x-1\right)\)
a) x2 -y2 +4y-4
= x2 - (y2- 4y+4)
= x2 - (y-2)2
=(x+y-2).(x-y+2)
b) 8x^3-1
= (2x)3 -13
= (2x-1). (4x2 +2x+1)
c) x^2-x-42
= x2 +6x -7x -42
= x.(x+6) - 7. (x+6)
=(x+6).(x-7)
d) x^2-4x-5
= x2+x -5x-5
= x.(x+1) - 5.(x+1)
=(x-5).(x+1)
e) 6x^2-x-5
= (6x2 -6x) + (5x-5)
= 6x.(x-1) + 5.(x-1)
= (6x+5).(x-1)
c) \(x^2-x-42=x^2+6x-7x-42\)
\(=x\left(x+6\right)-7\left(x+6\right)\)
\(=\left(x-7\right)\left(x+6\right)\)
a ) \(x^2-y^2+4y-4=x^2-\left(y^2-4y+4\right)=x^2-\left(y-2\right)^2=\left(x-y+2\right)\left(x+y-2\right)\)
b ) \(8x^3-1=\left(2x-1\right)\left(4x^2+2x+1\right)\)
c ) \(x^2-x-42=x^2+6x-7x-42=x\left(x+6\right)-7\left(x+6\right)=\left(x-7\right)\left(x+6\right)\)
d ) \(x^2-4x-5=x^2-5x+x-5=x\left(x-5\right)+x-5=\left(x+1\right)\left(x-5\right)\)
e ) \(6x^2-x-5=6x^2-6x+5x-5=6x\left(x-1\right)+5\left(x-1\right)=\left(6x+5\right)\left(x-1\right)\)
d) \(x^2-4x-5=x^2-5x+x-5\)
\(=x\left(x-5\right)+\left(x-5\right)\)
\(=\left(x+1\right)\left(x-5\right)\)
e) \(6x^2-x-5\)
\(=6x^2-6x+5x-5\)
\(=6x\left(x-1\right)+5\left(x-1\right)\)
\(=\left(6x+5\right)\left(x-1\right)\)
