Question

Zapisz w jak najprostszej postaci:

a)(x+1)(x-2)+(x+2)(x-1)
b)(5k+n)(k-2n)-k(4k+n)
c)(4y+3)(y-2)-2y(4-2y)
d)2a(3a²-1)-(a²+2)(a+2)
e)5x²(x²+1)-(x²-2(x²+3)
f)(4p-3r)(p+2r)-(3p-r)(p+6r)
g)4(2a-b)(2a+4b)-(3a-2b)(3b-2a)
h)2d²-(3c-2d)(c-d)-c(c-2d)+2d²

Answer 1

A)(x+1)(x-2)+(x+2)(x-1)=x^+2x+x-2+(x^-x+2x-2)=x^+2x^-2+x^-x+2x-2=4x^+x-4
b)(5k+n)(k-2n)-k(4k+n)=5k^-10kn+kn-2n^-4k^-kn=k^-2n^-10kn
c)(4y+3)(y-2)-2y(4-2y)=4y^-8y+3y-6-8y+4y^=8y^-13y-6
d)2a(3a²-1)-(a²+2)(a+2)= 6a/-2a-(a/+2a^+2a+4)=6a/-2a-a/-2a^-2a-4=5a/-2a^-4a-4
f)(4p-3r)(p+2r)-(3p-r)(p+6r)=4p^+8pr-3pr-6r^-(3p^+18pr-pr-6r^)=4p^+5pr-6r^-3p^-18pr+pr+6r^=p^-12pr
g)4(2a-b)(2a+4b)-(3a-2b)(3b-2a)=4(4a^+8ab-2ba-4b^)-(9ab-6a^-6b^+4ba)=16a^+32ab-8ba-16b^-9ab+6a^+6b^-4ba=6a^+6b^-11ba
h)2d²-(3c-2d)(c-d)-c(c-2d)+2d² = 2d^-(3c^-3cd-2dc+2d^)-c^+2cd+2d^=2d^-3c^+3cd+dc-2d^-c^+2cd+2d^=-4c^+2d^+6cd

^-do kwadratu
/-do potęgi trzeciej

licze że się przyda, i na naj....

Answer 2

A)(x+1)(x-2)+(x+2)(x-1) = x^2-2x+x-2+x^2-x+2x-2=2x^2-4
b)(5k+n)(k-2n)-k(4k+n) = 5k^2 - 10kn + kn - 2n^2 - 4k^2 - kn= k^2 - 11kn - 2n^2
c)(4y+3)(y-2)-2y(4-2y) = 4y^2 - 8 + 3y - 6 - 8y + 4y^2 = 8y^2 - 14 - 5y
d)2a(3a²-1)-(a²+2)(a+2) = 6a^3 - 2a - (a^3 + 2a^2 + 2a + 4) = 6a^3 - 2a - a^3 - 2a^2 - 2a - 4 = 5a^3 - 2a^2 - 4
e)5x²(x²+1)-(x²-2)(x²+3) = 5x^4 + 5x^2 - ( x^4 + 3x^2 - 2x^2 -6) =5x^4 + 5x^2 - x^4 - 3x^2 - + 2x^2 + 6 = 4x^4 + 6
f)(4p-3r)(p+2r)-(3p-r)(p+6r) = 4p^2 + 8pr - 3pr - 6r^2 - (3p^2 + 18pr - pr - 6r^2) = 4p^2 + 8pr - 3pr - 6r^2 - 3p^2 - 18pr + pr + 6r^2 = p^2 - 12pr
g)4(2a-b)(2a+4b)-(3a-2b)(3b-2a) = 4(2a^2 + 8ab - 2ab - 4b^2) - (9ab - 6a^2 - 6b^2 + 4ab) = 8a^2 + 32ab - 8ab - 16b^2 - 9ab + 6a^2 +6b^2 - 4ab = 14a^2 +11ab - 10b^2
h)2d²-(3c-2d)(c-d)-c(c-2d)+2d² = 2d^2 - (3c^2 - 3cd - 2cd +2d^2) - c^2 +2cd +2d^2 = 2d^2 - 3c^2 +3cd + 2cd - 2d^2 - c^2 + 2cd +2d^2 = 2c^2 + 7cd

Oznaczenie np 2d^2 - oznacza podniesienie do kwadratu. Myślę że zadanie jest zrozumiałe. Jeżeli jakieś pytania to proszę pisać.