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imagewidth (px) 2
3.75k
| material_type
stringclasses 2
values | latex
sequencelengths 1
1
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"good"
] |
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"9. $\\displaystyle {x}^{3}-{y}^{3}=(x-y)({x}^{2}+xy+{y}^{2})$"
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"$\\displaystyle =2 \\sqrt{7}\\left\\{(3+\\sqrt{7})^{2}+2+(3-\\sqrt{7})^{2}\\right\\}$"
] |
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"$\\displaystyle =2 \\sqrt{7} \\times 34$"
] |
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"$\\displaystyle =68 \\sqrt{7}$"
] |
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HW | [
"$\\displaystyle =68 \\sqrt{7}$"
] |
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HW | [
"good."
] |
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"$\\displaystyle =27-9$"
] |
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"$\\displaystyle =18$"
] |
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"$\\displaystyle x^{3}-y^{3}=(x-y)^{3}+3 x y(x-y)$"
] |
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"$\\displaystyle x-y=5+\\sqrt{7}-(5-\\sqrt{7})=2 \\sqrt{7}$"
] |
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"$\\displaystyle =56 \\sqrt{7}+108 \\sqrt{7}$"
] |
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"20. $\\displaystyle A \\ast B = 9A - 9B$"
] |
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"$\\displaystyle 9\\left(x^{2}+2 x+9y+1\\right)-9(-2 x-y-8)$"
] |
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"$\\displaystyle =9 x^{2}+18 x+81y+9+18 x+9y+72$"
] |
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"$\\displaystyle x+y=1, \\quad x y=-3$"
] |
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HW | [
"$\\displaystyle x^{2}-x y+y^{2}=(x+y)^{2}-3 x y$"
] |
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"$\\displaystyle x^{2}-x y+y^{2}=(x+y)^{2}-3 x y$"
] |
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"$\\displaystyle =1^{2}-3 \\times(-3)$"
] |
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HW | [
"$\\displaystyle =1^{2}-3 \\times(-3)$"
] |
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"$\\displaystyle =1+9$"
] |
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"$\\displaystyle \\frac{x^{4}+5 x^{3}+12 x^{2}+20 x+7}{A}$"
] |
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HW | [
"$\\displaystyle \\frac{x^{4}+5 x^{3}+12 x^{2}+20 x+7}{A}$"
] |
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"$\\displaystyle \\doteq x^{2}+3 x+1 \\quad \\cdots \\quad 3 x+2$"
] |
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HW | [
"$\\displaystyle \\doteq x^{2}+3 x+1 \\quad \\cdots \\quad 3 x+2$"
] |
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"$\\displaystyle x^{4}+5 x^{3}+12 x^{2}+20 x+7$"
] |
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"$\\displaystyle 16=8-2 x y$"
] |
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"$\\displaystyle 16=8-2 x y$"
] |
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"$\\displaystyle =-4(8-4)$"
] |
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"$\\displaystyle =-4(8-4)$"
] |
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"$\\displaystyle =-16$"
] |
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"$\\displaystyle P(x)=\\left(x^{2}-2 x+1\\right)(x-2)-3 x+6$"
] |
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HW | [
"$\\displaystyle P(x)=\\left(x^{2}-2 x+1\\right)(x-2)-3 x+6$"
] |
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"$\\displaystyle =x^{3}-2 x^{2}-2 x^{2}-4 x+x-2-3 x+6$"
] |
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"$\\displaystyle x^{3}-4 x^{2}-6 x+4$"
] |
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"$\\displaystyle $"
] |
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HW | [
"$\\displaystyle $"
] |
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"$\\displaystyle =x^{3}-4 x^{2}+2 x+4$"
] |
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HW | [
"$\\displaystyle =x^{3}-4 x^{2}+2 x+4$"
] |
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"$\\displaystyle =\\frac{(1+5)(1-5)\\left(1^{2}+5^{2}\\right)\\left(1^{4}+5^{4}\\right)}{4}=\\frac{\\left(1^{2}-5^{2}\\right)\\left(1^{2}+5^{2}\\right)\\left(1^{4}+5^{4}\\right)}{4}=\\frac{\\left(1^{4}-5^{4}\\right)(1^{4}+5^{4})}{4}= \\frac{\\left(1^{8}-5^{8}\\right)}{4}=-\\frac{\\left(5^{8}-1^{8}\\right)}{4}$"
] |
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"Good!\n"
] |
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HW | [
"perfect!"
] |
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HW | [
"perfect!"
] |
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"$\\displaystyle 1=x^{3}-y^{3}-12$"
] |
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"$\\displaystyle 1=x^{3}-y^{3}-12$"
] |
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HW | [
"3)"
] |
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HW | [
"3)"
] |
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"$\\displaystyle c-a=-(a-b+b-c)=-5$"
] |
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"$\\displaystyle c-a=-(a-b+b-c)=-5$"
] |
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"$\\displaystyle \\frac{1}{2}\\left\\{(a-b)^{2}+(b-c)^{2}+(c-a)^{2}\\right\\}$"
] |
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"$\\displaystyle =\\frac{1}{2}\\left\\{9+4+(-5)^{2}\\right\\}$"
] |
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HW | [
"$\\displaystyle =19$"
] |
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HW | [
"$\\displaystyle 19$"
] |
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HW | [
"$\\displaystyle 19$"
] |
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HW | [
"Perfect!!"
] |
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HW | [
"$\\displaystyle x+y=-7, \\quad xy=7$"
] |
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HW | [
"$\\displaystyle x+y=-7, \\quad xy=7$"
] |
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HW | [
"$\\displaystyle x^{2}-x y+y^{2}=(x+y)^{2}-3 x y$"
] |
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HW | [
"$\\displaystyle x^{2}-x y+y^{2}=(x+y)^{2}-3 x y$"
] |
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HW | [
"$\\displaystyle x^{2}-x y+y^{2}=49-21=28$"
] |
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HW | [
"$\\displaystyle x^{2}-x y+y^{2}=49-21=28$"
] |
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HW | [
"$\\displaystyle 28$"
] |
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HW | [
"Good !"
] |
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HW | [
"Good !"
] |
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HW | [
"$\\displaystyle 7 x^{3}-8 x^{2}+7 x-4$"
] |
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HW | [
"$\\displaystyle 7 x^{3}-8 x^{2}+7 x-4$"
] |
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HW | [
"$\\displaystyle \\left(x^{2}+y\\right)^{2}(x-y)+x^{2} y-x y^{2}$"
] |
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HW | [
"$\\displaystyle \\left(x^{2}+y\\right)^{2}(x-y)+x^{2} y-x y^{2}$"
] |
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HW | [
"$\\displaystyle 8 \\times(-6)$"
] |
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HW | [
"$\\displaystyle -\\frac{1}{2}(10\\quad =-2(a b+b c+c a))$"
] |
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HW | [
"$\\displaystyle -\\frac{1}{2}(10\\quad =-2(a b+b c+c a))$"
] |
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HW | [
"$\\displaystyle -5=a b+b c+c a$"
] |
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HW | [
"$\\displaystyle a^{4}+b^{4}+c^{4}=\\left(a^{2}+b^{2}+c^{2}\\right)^{2}$"
] |
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HW | [
"$\\displaystyle =10^{2}$"
] |
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HW | [
"$\\displaystyle =10^{2}$"
] |
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HW | [
"$\\displaystyle =100$"
] |
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HW | [
"$\\displaystyle =100$"
] |
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HW | [
"$\\displaystyle \\left(4 a^{2}+25 b^{2}+c^{2}+5 b c-10 a b-2 a c\\right)$"
] |
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HW | [
"$\\displaystyle \\left(4 a^{2}+25 b^{2}+c^{2}+5 b c-10 a b-2 a c\\right)$"
] |
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HW | [
"$\\displaystyle \\left(4 a^{2}+25 b^{2}+c^{2}-10 a b-5 b c+2 a c\\right)$"
] |
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HW | [
"$\\displaystyle \\left(4 a^{2}+25 b^{2}+c^{2}+10 a b-5 b c-2 a c\\right)$"
] |
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HW | [
"$\\displaystyle \\left(4 a^{2}+25 b^{2}+c^{2}+10 a b-5 b c-2 a c\\right)$"
] |
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HW | [
"$\\displaystyle =16 a^{2}+100 b^{2}+4 c^{2}$"
] |
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HW | [
"$\\displaystyle =16 a^{2}+100 b^{2}+4 c^{2}$"
] |
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HW | [
"$\\displaystyle 16 a^{2}+100 b^{2}+4 c^{2}$"
] |
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HW | [
"$\\displaystyle 5 x+4 x^{2}-2x y+8 y^{2}=-9 x^{2}+6 x y-18 y^{2}$"
] |
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HW | [
"$\\displaystyle 5 x=-13 x^{2}+8 x y-26 y^{2}$"
] |
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HW | [
"$\\displaystyle (a+b)^{2}=a^{2}+2 a b+b^{2}$"
] |
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HW | [
"$\\displaystyle (a+b)^{2}=a^{2}+2 a b+b^{2}$"
] |
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HW | [
"$\\displaystyle 9 x^{2}+12 x+4$"
] |
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HW | [
"$\\displaystyle 9 x^{2}+12 x+4$"
] |
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HW | [
"$\\displaystyle 81 a^{2}-25$"
] |
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HW | [
"Hi my name is yundo!"
] |
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HW | [
"Perfect!!"
] |
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HW | [
"$\\displaystyle 4 b c+12 a c)=216 a^{2}+8 b^{2}-8 c^{2}$"
] |
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HW | [
"$\\displaystyle 4 b c+12 a c)=216 a^{2}+8 b^{2}-8 c^{2}$"
] |
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HW | [
"$\\displaystyle -12 a b(6 a+2 b-2 c)$"
] |
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HW | [
"$\\displaystyle =-72 a^{2} b-24 a b^{2}+24 a b c$"
] |
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HW | [
"$\\displaystyle =-72 a^{2} b-24 a b^{2}+24 a b c$"
] |
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HW | [
"$\\displaystyle \\therefore 216 a^{2}+8 b^{2}-8 c^{2}-72 a^{2} b-24 a b^{2}+$"
] |