Question

Wykonaj mnożenie:

a) (a+1)(a-1)

b) (x-15)(x-1)

c) (4+x)(x-8)

d) (3a-2b)(a+b)

e) 2(b-3c)(b+3c)

f) (+)(a-b) * 5

g) (-)(+

h) (+4)(4+)

i) (-5)(7x-2)(4+)

Answer 1

a) (a+1)(a-1)=a^2-1 - wzór skróc. mnożenia

b) (x-15)(x-1)=x^2-15x-x+15=x^2-16x+15

c) (4+x)(x-8)=4x-32+x^2-8x=x^2-4x-32

d) (3a-2b)(a+b)=3a^2+3ab-2ab-2b^2=3a^2+ab-2b^2

e) 2(b-3c)(b+3c)=2(b^2-9c^2)=2b^2-18c^2

f) (+)(a-b) * 5=5a^3-5a^2b+5ab^2-5b^2

g) (-)(+)=5-3=2

h) (+4)(4+)=4V7+7+16+4V7=8V7+23

i) (-5)(7x-2)(4+)=(21x^3-6x^2-35x-10)(4+)=

=84x^3 +126x^5 -24x^2 -36x^4 -140x -210x^3 -40-60x^2=

=126x^5-36x^4-126x^3-84x^2-140x-40

Answer 2

a)(a+1)(a-1)=a²-1

b)(x-15)(x-1)=x(x-1)-15(x-1)=x²-x-15x+15=x²-16x+15

c)(4+x)(x-8)=4(x-8)+x(x-8)=4x-32+x²-8x=x²-4x-32

d)(3a-2b)(a+b)=3a(a+b)-2b(a+b)=3a²+3ab-2ab-2b²=3a²+ab+b²

e)2(b-3c)(b+3c)=2(b²-9c²)=2b²-18c²

f)(a²+b²)(a-b)*5=[a²(a-b)+b²(a-b)]*5=5[a³-a²b+ab²-b³]=5a³-5a²b+5ab²-5b³

g)(√5-√3)(√5+√3)=5-3=2

h)(√7+4)(4+√7)=√7(4+√7)+4(4+√7)=4√7+7+16+4√7=23+8√7

i)(3x²-5)(7x-2)(4+6x²)=4[3x²(7x-2)-5(7x-2)]+6x²[3x²(7x-2)-5(7x-2)]=

    4[21x³-6x²-35x +10]+6x²[21x³-6x²-35x+10]=81x³-24x²-140x+40+126x⁵-36x⁴-210x³+60x²=126x⁵-36x⁴-129x³+36x²-140x+40

 

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