Question

Zastosuj wzory skróconego mnożenia. (Obliczenia)

Uprość wyrażenie:

a) (5y+1)(1-5y)-(1+5y)²=

b) (x-3)(x+3)+(2+x)(2-x)=

c) (2y-3)²-(3y-2)(3y+2)=

d) (2x-y)(2x+y)+(3x+2y)(3x-2y)=

e) (y+3x)(3x-y)-(x-5y)(x+5y)=

Answer 1

a)

(5y+1)(1-5y) -(1+5y)^2 =(1+5y)(1-5Y) -(1+5y)^2 =

=1-25y^2 -(1+10y+25y^2) =1-25y^2-1-10y - 25y^2=

= -50y^2 -10y = -10(5y^2+y) = -10y(5y+1)

b)

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

c)

(2y-3)^2 -(3y-2)(3y+2) =4y^2-12y +9 -(9y^2 -4) =

= 4y^2 -12y +9 -9y^2 +4 = -5y^2 -12y +13

d)

(2x-y)(2x+y) +(3x+2y)(3x-2y) =4x^2 -y^2 +9x^2 -4y^2 =13x^2 -5y^2

e)

(y+3x)(3x-y) -(x-5y)(x+5y) =(3x+y)(3x-y) -(x-5y)(x+5y) =

=9x^2 -y^2 -(x^2 -25y^2) = 9x^2 - y^2 -x^2 +25y^2 =

= 8x^2 + 24y^2 = 8(x^2 +3y^2)