a, \(x^2-4x-5\)
\(=x^2-5x+x-5=x\left(x-5\right)+\left(x-5\right)\)
\(=\left(x+1\right)\left(x-5\right)\)
b, \(x^2-4xy+4y^2-36\)
\(=\left(x-2y\right)^2-36=\left(x-2y-6\right)\left(x-2y+6\right)\)
c, \(x^2-9x+20=x^2-5x-4x+20\)
\(=x\left(x-5\right)-4\left(x-5\right)\)
\(=\left(x-4\right)\left(x-5\right)\)
d, \(\left(9x^2-36\right)-\left(3x-6\right)\left(2x+5\right)\)
\(=\left(3x-6\right)\left(3x+6\right)-\left(3x-6\right)\left(2x+5\right)\)
\(=\left(3x-6\right)\left(3x+6-2x-5\right)\)
\(=3\left(x-2\right)\left(x+1\right)\)
a) \(x^2-4x-5=x^2-4x+4-9\)
= \(\left(x-2\right)^2-3^2\)
= \(\left(x-2-3\right)\left(x-2+3\right)=\left(x-5\right)\left(x+1\right)\)
b) \(x^2-4xy+4y^2-36\)
= \(\left(x-2y\right)^2-6^2=\left(x-2y-6\right)\left(x-2y+6\right)\)
c) \(x^2-9x+20\)
= \(\left(x-5\right)\left(x-4\right)\)
d) \(\left(9x^2-36\right)-\left(3x-6\right)\left(2x+5\right)\)
= \(\left(3x-6\right)\left(3x+6\right)-\left(3x-6\right)\left(2x+5\right)\)
= \(\left(3x-6\right)\left(3x+6-2x-5\right)=\left(3x-6\right)\left(x+1\right)\)
a) \(x^2-4x-5=x^2+x-5x-5=x\left(x+1\right)-5\left(x+1\right)=\left(x-5\right)\left(x+1\right)\)
b) \(x^2-4xy+4y^2-36=\left(x-2y\right)^2-36=\)
c) \(x^2-9x+20=x^2-4x-5x+20=x\left(x-4\right)-5\left(x-4\right)=\left(x-5\right)\left(x-4\right)\)
d) \(\left(9x^2-36\right)-\left(3x-6\right)\left(2x+5\right)=9x^2-36-\left(6x^2+15x-12x-30\right)\)
= \(9x^2-36-6x^2-15x+12x+30=3x^2-3x-6\)
= \(3x^2+3x-6x-6=3x\left(x+1\right)-6\left(x+1\right)=\left(3x-6\right)\left(x+1\right)\)
a)x2-4x-5=x2+x-5x-5=(x2+x)-(5x+5)=x(x+1)-5(x+1)=(x-5)(x+1)
b)x2-4xy+4y2-36=[x2-2x2y+(2y)2]-36=(x-2y)2-36=(x-2y-6)(x-2y+6)
c)x2-9x+20=x2-4x-5x+20=(x2-4x)-(5x-20)=x(x-4)-5(x-4)=(x-5)(x-4)
d)(9x2-36)-(3x-6)(2x+5)=(3x-6)(3x+6)-(3x-6)(2x+5)=(3x-6)(3x+6-2x-5)=3(x-2)(x+1)