c) Ta có: \(33\cdot55+33\cdot67+45\cdot33+67\cdot67\)

\(=33\left(55+45\right)+67\left(33+67\right)\)

\(=33\cdot100+67\cdot100\)

\(=100\cdot100=10000\)

1

a,

=(202+54).(202-54)+256.352

=37888+256.352

=37888+90112

=128000

b,

=621-769.373-21904

=621-286837-21904

=-308120

c,

42^2-10^2/(36,5)^2-(27,5)^2

=(42-10).(42+10)/(36,5-27,5).(27,5+36,5)

=1664/576=2(8)

1. Tính nhanh :

a) \(202^2-54^2+256.352\)

\(=\left(202-54\right).\left(202+54\right)+256.352\)

\(=148.256+256.352\)

\(=256.\left(148+252\right)=256.400=102400\)

a,=(202-54)(202+54)+256*352=248.*256+256*352=256*(248+352)=256*600=256*6*100=153600

b. làm tương tự

c,=5/(1+2+...+10)=5.\(\frac{10.\left(10+1\right)}{2}\)=275

(ta có công thức 1+2+...+n=\(\frac{n.\left(n+1\right)}{2}\) dễ dàng chứng minh)

chỉ biết lm câu b thôi

5+10+15+20+25+30+35+40+45+50=5.(1+2+3+4=5+6+7+8+9+10)=55.5=5x50x5=250.5=1250

\(x^2+7x+12=x^2+3x+4x+12=x\left(x+3\right)+4\left(x+3\right)=\left(x+3\right)\left(x+4\right)=0\)

\(x^2+3x-18=0\Leftrightarrow x^2-3x+6x-18=x\left(x-3\right)+6\left(x-3\right)=\left(x+6\right)\left(x-3\right)=0\)

b) \(x^2-10x+16\)

\(=x^2-2x-8x+16\)

\(=x\left(x-2\right)-8\left(x-2\right)\)

\(=\left(x-2\right)\left(x-8\right)\)

c) \(x^2+6x+8\)

\(=x^2+2x+4x+8\)

\(=x\left(x+2\right)+4\left(x+2\right)\)

\(=\left(x+2\right)\left(x+4\right)\)

d) tươn tự c

e) \(x^2+3x-18=0\)

\(\Leftrightarrow x^2+6x-3x-18=0\)

\(\Leftrightarrow x\left(x+6\right)-3\left(x+6\right)=0\)

\(\Leftrightarrow\left(x+6\right)\left(x-3\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x+6=0\\x-3=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=-6\\x=3\end{cases}}}\)

Vậy ,...

f) \(8x^2+30x+7=0\)

\(\Leftrightarrow8x^2+28x+2x+7=0\)

\(\Leftrightarrow4x\left(2x+7\right)+\left(2x+7\right)=0\)

\(\Leftrightarrow\left(2x+7\right)\left(4x+1\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}2x+7=0\\4x+1=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=\frac{-7}{2}\\x=\frac{-1}{4}\end{cases}}}\)

Vậy ...

g) \(x^3-11x^2+30x=0\)

\(\Leftrightarrow x^3-5x^2-6x^2+30x=0\)

\(\Leftrightarrow x^2\left(x-5\right)-6x\left(x-5\right)=0\)

\(\Leftrightarrow\left(x-5\right)\left(x^2-6x\right)=0\)

\(\Leftrightarrow x\left(x-5\right)\left(x-6\right)=0\)

\(\Leftrightarrow x=0\)hoặc x=5 hoặc x=6

Vậy ...