5m²+5mn-3mn-3n²-5m²=2mn-3n²
1. x= от 2 до 4, тоесть 2,3 или 4.
2. x= от 1 до 5, тоесть 1,2,3,4 или 5.
<span>Выполните действия:
</span>
![1) ( x^{4} )^7= x^{(4*7)}= x^{28} \\ 2) (3 x^{6} )^3=3^3* x^{6*3}=27 x^{18}](https://tex.z-dn.net/?f=1%29+%28+x%5E%7B4%7D+%29%5E7%3D+x%5E%7B%284%2A7%29%7D%3D+x%5E%7B28%7D+%5C%5C+2%29++%283+x%5E%7B6%7D+%29%5E3%3D3%5E3%2A+x%5E%7B6%2A3%7D%3D27+x%5E%7B18%7D++)
Упростите выражение:
![1) 4a^2c(-2.5ac^4)=4*(-2.5)*a ^{(2+1)} *c^{(1+4)} =-10a^3c^5 \\ 2)(-2 x^{10}y^6 )^4=(-2^4)* x^{(10*4)}*y ^{(6*4)}=16 x^{40} y^{24}](https://tex.z-dn.net/?f=1%29+4a%5E2c%28-2.5ac%5E4%29%3D4%2A%28-2.5%29%2Aa+%5E%7B%282%2B1%29%7D+%2Ac%5E%7B%281%2B4%29%7D+%3D-10a%5E3c%5E5+%5C%5C+2%29%28-2+x%5E%7B10%7Dy%5E6+%29%5E4%3D%28-2%5E4%29%2A+x%5E%7B%2810%2A4%29%7D%2Ay+%5E%7B%286%2A4%29%7D%3D16+x%5E%7B40%7D+y%5E%7B24%7D++++)
223
1). ...=
![\frac{(97+83)( 97^{2} - 97*83 + 83^{2}) }{180} + 97*83](https://tex.z-dn.net/?f=+%5Cfrac%7B%2897%2B83%29%28+97%5E%7B2%7D+-+97%2A83+%2B+83%5E%7B2%7D%29+%7D%7B180%7D+%2B+97%2A83)
=
![97^{2} - 97*83 + 83^{2} + 97*83 = 9409 + 6889 = 16298](https://tex.z-dn.net/?f=97%5E%7B2%7D+-+97%2A83+%2B+83%5E%7B2%7D+%2B+97%2A83+%3D+9409+%2B+6889+%3D+16298)
2)...=
![\frac{(71+49)( 71^{2} - 71*49 + 49^{2}) }{120} + 71*49](https://tex.z-dn.net/?f=+%5Cfrac%7B%2871%2B49%29%28+71%5E%7B2%7D+-+71%2A49+%2B+49%5E%7B2%7D%29+%7D%7B120%7D+%2B+71%2A49)
=
![71^{2} - 71*49 + 49^{2} + 71*49 = 6241 + 2401 = 8642](https://tex.z-dn.net/?f=71%5E%7B2%7D+-+71%2A49%C2%A0%2B+49%5E%7B2%7D+%2B+71%2A49+%3D+6241+%2B+2401+%3D+8642)
3)...=
![\frac{(67+52)( 67^{2} - 67*52 + 52^{2}) }{119} + 67*52](https://tex.z-dn.net/?f=+%5Cfrac%7B%2867%2B52%29%28+67%5E%7B2%7D+-+67%2A52+%2B+52%5E%7B2%7D%29+%7D%7B119%7D+%2B+67%2A52)
=
![67^{2} - 67*52 + 52^{2} + 67*52 = 4489 + 2704 = 7183](https://tex.z-dn.net/?f=67%5E%7B2%7D+-+67%2A52%C2%A0%2B+52%5E%7B2%7D+%2B+67%2A52+%3D+4489+%2B+2704+%3D+7183)
4)...=
![\frac{(87 - 37)( 87^{2} + 87*37 + 37^{2}) }{50} - 87*37](https://tex.z-dn.net/?f=+%5Cfrac%7B%2887+-+37%29%28+87%5E%7B2%7D+%2B+87%2A37+%2B+37%5E%7B2%7D%29+%7D%7B50%7D+-+87%2A37)
=
![87^{2} + 87*37 + 37^{2} - 87*37 = 7569 + 1369 = 8938](https://tex.z-dn.net/?f=87%5E%7B2%7D+%2B+87%2A37%C2%A0%2B+37%5E%7B2%7D+-+87%2A37%C2%A0%3D+7569+%2B+1369+%3D+8938)
224
1). 2a^3 + 9 - 2(a+1)(a^2 - a + 1) = 2a^3 + 9 - 2(a^3 + 1) = 2a^3 + 9 - 2a^3 - 2 = 7
2). x(x+2)(x-2) - (x-3)(x^2+3x+9) = x(x^2 - 4) - (x^3 - 27) = x^3 - 4x - x^3 + 27 = -4x + 27 при х = 1/4: -4*1/4 + 27 = -1 + 27 = 26
3). 3(b-1)^3 + (b+2)(b^2-2b+4) - (b+1)^3 = 3(b^3 - 3b^2 + 3b - 1) + b^3 + 8 - (b^3 + 3b^2 + 3b + 1) = 3b^3 - 9b^2 + 9b - 3 + b^3 + 8 - b^3 - 3b^2 - 3b - 1 = 3b^3 - 12b^2 + 6b + 4
при b = -1/3
-3/27 - 12/9 - 6/3 + 4 = - 1/9 - 12/9 - 18/9 + 4 = -31/9 + 4 = (36-31)/9 = 5/9
4). (a-1)^3 - 4a(a+1)(a-1) + 3(a-1)(a^2+a+1) = a^3 - 3a^2 + 3a - 1 - 4a(a^2 - 1) + 3(a^3 - 1) = a^3 - 3a^2 + 3a - 1 - 4a^3 + 4 + 3a^3 - 3 = - 3a^2 + 3a
при а = -2
-3 * 4 + 3 * (-2) = -12 -6 = -18