Đáp án + Giải thích các bước giải:
`a, (x-3)(x+3)(x+2)-(x-1)(x^2-3)-5x(x-4)^2-(x-5)^2`
`=(x^2 - 9 )(x+2) - (x^3 - 3x -x^2 +3)-5x(x^2 - 8x + 16)-(x^2 - 10x + 25)`
`=x^3 + 2x^2 -9x-18-x^3 + 3x + x^2 - 3 - 5x^3 + 40x^2 - 80x - x^2 +10x-25`
`=(x^3-x^3 -5x^3)+(2x^2 +x^2+40x^2-x^2) + (-9x+3x-80x+10x) + (-18-3-25)`
`=-5x^3 + 42x^2 -76x-46`
`b, (x+5)(x^2 -5x+25)-(x+3)^3 +(x-2)(x^2 +2x+4)-(x-1)^3`
`=x^3 +125 - (x^3 + 9x^2 + 27x + 27 ) + x^3 - 8 -(x^3 - 3x^2 + 3x - 1)`
`=x^3 +125 - x^3 - 9x^2 - 27x - 27 +x^3 - 8 - x^3 + 3x^2 - 3x + 1`
`=(x^3 -x^3-x^3) + (-9x^2+3x^2) + (-27x-3x) + (-27+125-8+1)`
`=-x^3 - 6x^2 - 30x +91`
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Áp dụng :
HĐT:
`2,(A-B)^2= A^2 - 2AB+B^2`
`3,A^2 - B^2 = (A+B)(A-B)`
`4,(A+B)^3= A^3 + 3A^2B+3AB^2+B^3`
`5, (A-B)^3=A^3 - 3A^2B+3AB^2-B^3`
`6, A^3 + B^3 = (A+B)(A^2 -AB+B^2)`
`7, A^3 - B^3 = (A-B)(A^2 +AB+B^2)`
