Разложите на множители:а)x(x-4)-5(4-x)
b)b(b-1)+(1-b)
v)2(p-2)+p(2-p)
a) x^2 - 4x -20 + 5x = 0
x^2 +x - 20= 0
D = 1 +80 = 81 = 9^2
x1= (-1 - 9) /2
x1 = -5
x2= (-1+9)/2
x2 = 4
2) b^2 -b +1 - b= 0
b^2 - 2b +1 =0
d = 4 - 4 = 0
d1 = 2/2 = 1
3) 2p - 4 +2p - p^2
-p^2 +4p - 4=0
p^2 -4p +4=0
D= 16- 16= 0
P1= 4/2 = 2
а)x(x-4)-5(4-x)=x(x-4)+5(x-4)=(x-4)(x+5)
b)b(b-1)+(1-b)=b(b-1)-(b-1)=(b-1)(b-1)=(b-1)^2
v)2(p-2)+p(2-p) =-2(2-p)+p(2-p)=(2-p)(p-2)=-(2-p)(2+p)=-(4-p^2)=p^2-4
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Answers & Comments
a) x^2 - 4x -20 + 5x = 0
x^2 +x - 20= 0
D = 1 +80 = 81 = 9^2
x1= (-1 - 9) /2
x1 = -5
x2= (-1+9)/2
x2 = 4
2) b^2 -b +1 - b= 0
b^2 - 2b +1 =0
d = 4 - 4 = 0
d1 = 2/2 = 1
3) 2p - 4 +2p - p^2
-p^2 +4p - 4=0
p^2 -4p +4=0
D= 16- 16= 0
P1= 4/2 = 2
а)x(x-4)-5(4-x)=x(x-4)+5(x-4)=(x-4)(x+5)
b)b(b-1)+(1-b)=b(b-1)-(b-1)=(b-1)(b-1)=(b-1)^2
v)2(p-2)+p(2-p) =-2(2-p)+p(2-p)=(2-p)(p-2)=-(2-p)(2+p)=-(4-p^2)=p^2-4