3.Zamień na potęgę lub iloczyn.
a) a²+2ab+b²=
b) 9a²+3a+¼=
c) 25-36x²=
d) 16x²-8xy+y²=
4.Oblicz.
a) (3+2√2)²=
b) 3(√5-4)²=
c) 2(√2-5)²-3(√2+3)²=
5.Doprowadż do najprostszej postaci.
a) (2x-3y)²+(x-2y)(x+2y)=
b) x(x-1)²-x²(x-2)=
c) (m+2n)²-3(m-2n)²-5(m+2n)²=
d) 2[m(m+2)²-(m+1)(m-1)]-8m(m+1)=
e) 2[3(x-2y)-(x+y)²]+4[(x+2y)²-4(½x²-y+1)]
pierwiastki
usuń pierwiastek z mianownika
1/2√3=
2/√2+4²=
2/√5-(3/2)²=
oblicz
∛8/125=
4*√81/16 + 5*√64/25 - 2* ∛27/8=
(wszystko pod pierwiastkiem vały ulamek->) √36a²b do 4 dzielone c do 6
(√2+√8)²
(√18-√2)²
(√3-√2)(√3+√2)
(√2+√50)²-2²
3³*2³-(√2)²+4(√72-√2)²
(√3-5)(√3+3²)
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3.
a) a²+2ab+b²==(a+b)²
b) 9a²+3a+¼=(3a+1/2)²
c) 25-36x²=(5+6x)(5-6x)
d) 16x²-8xy+y²=(4x-y)²
4.Oblicz.
a) (3+2√2)²=9+12√2+8=17+12√2
b) 3(√5-4)²=3*(5-8√5+16)=3*(21-8√5)=63-24√5
c) 2(√2-5)²-3(√2+3)²=2*(2-10√2+25)-3*(2+6√2+9)=2*(27-10√2)-3*(11+6√2)= =54-20√2-33-18√2=21-38√2
5.Doprowadż do najprostszej postaci.
a) (2x-3y)²+(x-2y)(x+2y)=4x²-12xy+9y²+x²-4y²=5x²-12xy+5y²
b) x(x-1)²-x²(x-2)=x(x²-2x+1)-x³+2x²=x³-2x²+x-x³+2x²=x
c) (m+2n)²-3(m-2n)²-5(m+2n)²=m²+4mn+4n²-3*(m²-4nm+4n²)-5*(m²+4mn+4n²)= m²+4mn+4n²-3m²+12nm-12n²-5m²-20mn-20n²=-7m²-4mn-28n²
d) 2[m(m+2)²-(m+1)(m-1)]-8m(m+1)=2*[m(m²+4m+4)-(m²-1)]-8m²-1= =2*[m³+4m²+4m-m²+1]-8m²-1=2m³+6m²+8m+2-8m²-1=2m³-2m²+8m+1
e) 2[3(x-2y)-(x+y)²]+4[(x+2y)²-4(½x²-y+1)]=2[3x-6y-(x²+2xy+y²)]+4[(x²+4xy+4y²)-2x²+4y-4=2*(3x-6y-x²-2xy-y²)+4*(x²+4xy+4y²-2x²+4y)= 6x-12y-2x²-4xy-2y²+4x²+16xy+16y²-8x²+16y=6x+4y-6x²+12xy+14y²+16y