202² - 54² + 256.352

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

= 148.256 + 256.352

= 256.(148 + 352)

= 256.500

= 128.2.500

= 128.1000

= 128000

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)

các bạn ơi giúp mình với, chiều nay mình phải đi học rồi

2a) x^3+8=x^3+2^3

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

b)(3x+15)^2-(x-7)^2

=(3x+15-x+7)(3x+15+x-7)

=(2x+22)(4x+8)

=8(x+11)(x+2)

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

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

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 ...

A = \(\dfrac{2}{300}\) + \(\dfrac{6}{300}\) + \(\dfrac{10}{300}\)+.....+ \(\dfrac{202}{300}\) + \(\dfrac{206}{300}\)

A = \(\dfrac{1}{300}\)\(\times\) ( 2 + 6 + 10 +.....+ 202 + 206)

A = \(\dfrac{1}{300}\) \(\times\) ( 206 +2) \(\times\) { ( 206 - 2) : 4 + 1} : 2

A = \(\dfrac{1}{300}\) x 208 x 52 : 2

A = \(\dfrac{1352}{75}\)

B = \(\dfrac{24\times36+24\times64}{12\times135-12\times35}\)

B = \(\dfrac{24\times(36+64)}{12\times(135-35)}\)

B = \(\dfrac{24\times100}{12\times100}\)

B = 2