image imagewidth (px) 2 3.75k | material_type stringclasses 2
values | latex listlengths 1 1 |
|---|---|---|
HW | [
"$\\displaystyle -4 a b-3 a c-12 b c)$"
] | |
HW | [
"$\\displaystyle =1-(-5 b+1)^{2}+6 b(-5 b+1)-25 b^{2}$"
] | |
HW | [
"$\\displaystyle =1-\\left(25 b^{2}-10 b+1\\right)-30 b^{2}+6 b-25 b^{2}$"
] | |
HW | [
"$\\displaystyle =1-\\left(25 b^{2}-10 b+1\\right)-30 b^{2}+6 b-25 b^{2}$"
] | |
HW | [
"$\\displaystyle =-80 b^{2}+16 b=2 a b$"
] | |
HW | [
"$\\displaystyle =-80 b^{2}+16 b=2 a b$"
] | |
HW | [
"$\\displaystyle =k\\left(-\\frac{5}{3} b+\\frac{1}{3}\\right) b$"
] | |
HW | [
"$\\displaystyle =k\\left(-\\frac{5}{3} b+\\frac{1}{3}\\right) b$"
] | |
HW | [
"$\\displaystyle k=3\\cdot16=48$"
] | |
HW | [
"$\\displaystyle 48$"
] | |
HW | [
"$\\displaystyle 48$"
] | |
HW | [
"$\\displaystyle 25 b^{2}+(k-17) a b+4 a^{2}-1=0$"
] | |
HW | [
"$\\displaystyle (5 b+2 a+1)(5 b+2 a-1)=0$"
] | |
HW | [
"$\\displaystyle 25 b^{2}+5 b(2 a+1+2 a-1)+(2 a+1)(2 a-1)$"
] | |
HW | [
"$\\displaystyle =25 b^{2}+4 a \\cdot 5 b+4 a^{2}-1=0$"
] | |
HW | [
"$\\displaystyle \\therefore k-17=20 \\rightarrow k=37$"
] | |
HW | [
"$\\displaystyle \\therefore k-17=20 \\rightarrow k=37$"
] | |
HW | [
"$\\displaystyle 37$"
] | |
HW | [
"$\\displaystyle 37$"
] | |
HW | [
"$\\displaystyle \\therefore(9 x-y)(x-2y)$"
] | |
HW | [
"$\\displaystyle \\therefore(9 x-y)(x-2y)$"
] | |
HW | [
"$\\displaystyle =\\left(x^{2}+y^{2}\\right)^{2}-(x y)^{2}$"
] | |
HW | [
"$\\displaystyle =\\left(x^{2}+x y+y^{2}\\right)\\left(x^{2}-x y+y^{2}\\right)$"
] | |
HW | [
"$\\displaystyle =\\left(x^{2}+x y+y^{2}\\right)\\left(x^{2}-x y+y^{2}\\right)$"
] | |
HW | [
"$\\displaystyle =100+6=106 .$"
] | |
HW | [
"$\\displaystyle =100+6=106 .$"
] | |
HW | [
"$\\displaystyle \\left(x^{2}+x y+y^{2}\\right)\\left(x^{2}-x y+y^{2}\\right)$"
] | |
HW | [
"$\\displaystyle \\left(x^{2}+x y+y^{2}\\right)\\left(x^{2}-x y+y^{2}\\right)$"
] | |
HW | [
"$\\displaystyle =(106+3)(106-3)$"
] | |
HW | [
"$\\displaystyle 11227$"
] | |
HW | [
"$\\displaystyle 11227$"
] | |
HW | [
"$\\displaystyle x^{2}+(2 y+6) x-\\left(3 y^{2}-2 y-8\\right)$"
] | |
HW | [
"$\\displaystyle x^{2}+(2 y+6) x-\\left(3 y^{2}-2 y-8\\right)$"
] | |
HW | [
"$\\displaystyle =(x-y+2)(x+3 y+4)$"
] | |
HW | [
"$\\displaystyle \\therefore(x-y+2)(x+3 y+4)$"
] | |
HW | [
"$\\displaystyle \\therefore(x-y+2)(x+3 y+4)$"
] | |
HW | [
"$\\displaystyle (x-y+2)(x+3y+4)$"
] | |
HW | [
"$\\displaystyle (x-y+2)(x+3y+4)$"
] | |
HW | [
"$\\displaystyle 2 a=22 . \\quad a=11 .$"
] | |
HW | [
"$\\displaystyle 2 a=22 . \\quad a=11 .$"
] | |
HW | [
"$\\displaystyle p(x)=x^{3}-10 x^{2}+11 x+70 .$"
] | |
HW | [
"$\\displaystyle p(x)=x^{3}-10 x^{2}+11 x+70 .$"
] | |
HW | [
"$\\displaystyle p(x)=(x+2)(x-5)(x-7)$"
] | |
HW | [
"$\\displaystyle p(x)=(x+2)(x-5)(x-7)$"
] | |
HW | [
"$\\displaystyle (x+2)(x-5)(x-7)$"
] | |
HW | [
"$\\displaystyle x^{2}\\left(x^{2}-11 x+30-\\frac{11}{x}+\\frac{1}{x^{2}}\\right)$"
] | |
HW | [
"$\\displaystyle x^{2}\\left(x^{2}-11 x+30-\\frac{11}{x}+\\frac{1}{x^{2}}\\right)$"
] | |
HW | [
"$\\displaystyle =x^{2}\\left(x+\\frac{1}{x}-4\\right)\\left(x+\\frac{1}{x}-7\\right)$"
] | |
HW | [
"$\\displaystyle =x^{2}\\left(x+\\frac{1}{x}-4\\right)\\left(x+\\frac{1}{x}-7\\right)$"
] | |
HW | [
"$\\displaystyle \\|$\n$\\displaystyle 0$"
] | |
HW | [
"$\\displaystyle a^{6}+7 a^{2}-a^{4}-7 a$"
] | |
HW | [
"$\\displaystyle =a^{6}-a^{4}+7 a^{2}-7 a$"
] | |
HW | [
"$\\displaystyle =a^{4}(a^{2}-1)+7 a(a-1)$"
] | |
HW | [
"$\\displaystyle =a(a-1)\\left(a^{4}(a+1)+7\\right)$"
] | |
HW | [
"$\\displaystyle =a(a-1)\\left(a^{5}+a^{4}+7\\right)$"
] | |
HW | [
"$\\displaystyle =a(a-1)\\left(a^{5}+a^{4}+7\\right)$"
] | |
HW | [
"$\\displaystyle a,(a-1),\\left(a^{5}+a^{4}+7\\right)$"
] | |
HW | [
"$\\displaystyle =\\left(x^{2}+14\\right)^{2}-(4 x)^{2}$"
] | |
HW | [
"$\\displaystyle \\left(x^{2}+4 x+14\\right)\\left(x^{2}-4 x+14\\right)$"
] | |
HW | [
"$\\displaystyle \\left(x^{2}+4 x+14\\right)\\left(x^{2}-4 x+14\\right)$"
] | |
HW | [
"good!"
] | |
HW | [
"good!"
] | |
HW | [
"$\\displaystyle =(a+3 b+4 c)\\left(a^{2}+9 b^{2}+16 c^{2}-3 a b\\right.$"
] | |
HW | [
"$\\displaystyle a^{3}-b^{3}=(a-b)\\left(a^{2}+a b+b^{2}\\right)$"
] | |
HW | [
"$\\displaystyle (a-3 b)\\left(a^{2}+3 a b+9 b^{2}\\right)$"
] | |
HW | [
"$\\displaystyle a^{3}-8$"
] | |
HW | [
"$\\displaystyle a^{3}-8$"
] | |
HW | [
"$\\displaystyle =a^{3}-2^{3}$"
] | |
HW | [
"$\\displaystyle (a-2)\\left(a^{2}+2 a+4\\right)$"
] | |
HW | [
"$\\displaystyle a^{3}+b^{3}+c^{3}=3 a b c$"
] | |
HW | [
"$\\displaystyle a^{3}+b^{3}+c^{3}=3 a b c$"
] | |
HW | [
"$\\displaystyle \\frac{19\\left(a^{3}+b^{3}+c^{3}\\right)}{10 \\times 3 a b c}=\\frac{19}{10}$"
] | |
HW | [
"$\\displaystyle \\frac{19\\left(a^{3}+b^{3}+c^{3}\\right)}{10 \\times 3 a b c}=\\frac{19}{10}$"
] | |
HW | [
"$\\displaystyle \\therefore \\frac{19}{10}$"
] | |
HW | [
"$\\displaystyle \\therefore \\frac{19}{10}$"
] | |
HW | [
"$\\displaystyle x^{4}+16 x^{2} y^{2}+256 y^{4}$"
] | |
HW | [
"$\\displaystyle =\\left(x^{2}+16 y^{2}\\right)^{2}-(4 x y)^{2}$"
] | |
HW | [
"$\\displaystyle =\\left(x^{2}+16 y^{2}\\right)^{2}-(4 x y)^{2}$"
] | |
HW | [
"$\\displaystyle =\\left(x^{2}+4 x y+16 y^{2}\\right)\\left(x^{2}-4 x y+16 y^{2}\\right)$"
] | |
HW | [
"90. $\\displaystyle \\; 8{a}^{3}+48{a}^{2} b+96 a {b}^{2}+64 {b}^{3}$"
] | |
HW | [
"90. $\\displaystyle \\; 8{a}^{3}+48{a}^{2} b+96 a {b}^{2}+64 {b}^{3}$"
] | |
HW | [
"$\\displaystyle x^{2}+(10y-14 z) x+25 y^{2}-70 y z+49 z^{2}$"
] | |
HW | [
"$\\displaystyle x^{2}+(10y-14 z) x+25 y^{2}-70 y z+49 z^{2}$"
] | |
HW | [
"$\\displaystyle (x+5 y-7 z)^{2}$"
] | |
HW | [
"$\\displaystyle (x+5 y-7 z)^{2}$"
] | |
HW | [
"$\\displaystyle 9-(2 a)^{2}+3 b \\cdot 2 a-25 b^{2}$"
] | |
HW | [
"$\\displaystyle 9-(2 a)^{2}+3 b \\cdot 2 a-25 b^{2}$"
] | |
HW | [
"$\\displaystyle =9-(-5 b+3)^{2}+5 b(-5 b+3)-25 b^{2}$"
] | |
HW | [
"$\\displaystyle =9-(-5 b+3)^{2}+5 b(-5 b+3)-25 b^{2}$"
] | |
HW | [
"$\\displaystyle =9-\\left(25 b^{2}-30 b+9\\right)-40 b^{2}+24 b-25 b^{2}$"
] | |
HW | [
"$\\displaystyle =-90 b^{2}+54 b = k \\cdot(-\\frac{5}{2} b+\\frac{3}{2}) b$"
] | |
HW | [
"$\\displaystyle =-90 b^{2}+54 b = k \\cdot(-\\frac{5}{2} b+\\frac{3}{2}) b$"
] | |
HW | [
"$\\displaystyle 36 .$"
] | |
HW | [
"$\\displaystyle 36 .$"
] | |
HW | [
"$\\displaystyle x^{3}-2 x^{2}+a x+b=(x-2)(x-5) Q(x)$"
] | |
HW | [
"$\\displaystyle x^{3}-2 x^{2}+a x+b=(x-2)(x-5) Q(x)$"
] | |
HW | [
"75"
] | |
HW | [
"$\\displaystyle 8-40+2 a-24=0$"
] | |
HW | [
"$\\displaystyle 8-40+2 a-24=0$"
] | |
HW | [
"$\\displaystyle (x-2)^{2}(x-6)$"
] |
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