Question

Stosując wzory skróconego mnożenia , rozłóż na czynniki wyrażenie :
a/

(6x+1)^2-(4-3x)^2

b/

(5x-1)^2-(3x+2)^2

c/

(7x+2y)^2-(8x+y)^2

Z góy dzięki !! ;)

Answer 1

a) =36x^2+12x+1-(16-24x+9x^2)=36x^2+12x+1-16+24x-9x^2=27x^2+36x-15

obliczamy to ze wzoru a^2-b^2=(a-b)(a+b)

(6x+1)^2-(4-3x)^2=(6x+1-4+3x)(6x+1+4-3x)=(9x-3)(3x+5)

b) =25x^2-10x+1-(9x^2+12x+4)= 25x^2-10x+1-9x^2-12x-4=16x^2-22x-3

(5x-1)^2-(3x+2)^2=(5x-1-3x-2)(5x-1+3x+2)=(2x-3)(8x+1)

c) = 49x^2+28xy +4y^2-(64x^2+16xy+y^2)=  49x^2+28xy +4y^2-64x^2-16y-y^2= -15x^2+12xy+3y^2

(7x+2y)^2-(8x+y)^2=(7x+2y-8x-y)(7x+2y+8x+y)=(y-x)(15x+3y)