Question

Упростить выражения :

(m+5)^2 -(m-5)^2

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

(x-6)^2 -9x^2

Answer 1

$(m+5)^2-(m-5)^2=[(m+5)+(m-5)][(m+5)-(m-5)]=\ =(m+5+m-5)(m+5-m+5)=2mcdot10=20m\\ (m+5)^2-(m-5)^2=(m^2+10m+25)-(m^2-10m+25)=\ =m^2+10m+25-m^2+10m-25=20m\\ ****************************************\\ (x+y)^2-(x-y)^2=[(x+y)+(x-y)][(x+y)-(x-y)]=\ =(x+y+x-y)(x+y-x+y)=2xcdot2y=4xy\\ (x+y)^2-(x-y)^2=(x^2+2xy+y^2)-(x^2-2xy+y^2)=\ x^2+2xy+y^2-x^2+2xy-y^2=2xy+2xy=4xy\\ ***************************************$


$(x-6)^2-9x^2=(x-6)^2-(3x)^2=[(x-6)+3x][(x-6)-3x]=\ =(x-6+3x)(x-6-3x)=(4x-6)(-2x-6)=\ =2cdot(2x-3)cdot(-2)cdot(x+3)=-4(2x-3)(x+3)$