Question

a)5(x+2)^2-3(x-3)^2=(x+5)(x-5)= b)x(-2)(x+2)-(x-3)^2+(x+1)^2 c)2x+1)^2-(3x-1)(3x+1)=

Answer 1

a) 5(x+2)^2-3(x-3)^2-(x+5)(x-5)=5(x^2+4x+4)-3(x-3)^2-(x+5)(x-5)=5x^2+20x+20-3(x-3)^2-(x+5)(x-5)=5x^2+20x+20-3(x^2-6x+9)-(x+5)(x-5)=5x^2+20x+20-(3x^2-18x+27)-(x+5)(x-5)=5x^2+20x+20-3x^2+18x-27-(x+5)(x-5)=2x^2+20x+20+18x-27-(x+5)(x-5)=2x^2+38x+20-27-(x+5)(x-5)=2x^2+38x-7-(x+5)(x-5)=2x^2+38x-7-(x^2-25)=2x^2+38x-7-x^2+25=x^2+38x-7+25=x^2+38x+18

 

b) x(-2)(x+2)-(x-3)^2+(x+1)^2=(-x*2)(x+2)-(x-3)^2+(x+1)^2= -x*2(x+2)-(x-3)^2+(x+1)^2= -(x^2+x*2)*2-(x-3)^2+(x+1)^2= -(x^2*2+x*4)-(x-3)^2+(x+1)^2= -x^2*2-x*4-(x-3)^2+(x+1)^2= -x^2*2-x*4-(x^2-6x+9)+(x+1)^2= -x^2*2-x*4-x^2+6x-9+(x+1)^2= -3x^2-x*4+6x-9+(x+1)^2= -3x^2+2x-9+(x+1)^2= -3x^2+2x-9+x^2+2x+1= -2x^2+2x-9+2x+1= -2x^2+4x-9+1= -2x^2+4x-8

 

c) (2x+1)^2-(3x-1)(3x+1)=4x^2+4x+1-(3x-1)(3x+1)=4x^2+4x+1-(9x^2-1)=4x^2+4x+1-9x^2+1= -5x^2+4x+1+1= -5x^2+4x+2