Question

Zastosuj wzory skróconego mnożenia. 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=1-25y²-1-10y-25y²=-10y-50y²

 

b) (x-3)(x+3)+(2+x)(2-x)=x²-9+4-x²=-5

c) (2y-3)²-(3y-2)(3y+2)=4y²-12y-9-9y²+4=-5y²-12y-5

d) (2x-y)(2x+y)+(3x+2y)(3x-2y)=4x²-y²+9x²-4y²=13x²-5y²

e) (y+3x)(3x-y)-(x-5y)(x+5y)=9x²-y²-x²+25y²=8x²+24y²

Answer 2

Zastosuj wzory skróconego mnożenia. Uprość wyrażenie:

a) (5y+1)(1-5y)-(1+5y)²=

= (5y +1)*(-1)*(5y -1) - (1 + 10y +25y² =

= (-1)*(25y² -1) - 1 -10y -25y² =

= -25y² +1 -1 -10y -25y² =

= -50y² -10y =

= -10y(5y + 1)

 

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

= (x² -9) + (4 -x² ) =

= x² -9 +4 -x² =

=  -5

 

c) (2y-3)²-(3y-2)(3y+2)=

= 4y² -12y +9 -( 9y² - 4) =

= 4y² -12y +9 -9y² +4 =

=  -5y² -12y +13

 

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

=  4x² -y² + 9x² -4y² =

=  13x² - 5y²

 

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

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

= 9x² -y² -( x² -25y² ) =

= 9x² -y² -x² +25y² =

= 8x² +24y² =

= 8(x² +3y²)