3A:

a: \(75\cdot20.9+5^2\cdot20.9\)

\(=20.9\cdot100\)

=2090

b: \(86\cdot15+150\cdot1.4\)

\(=86\cdot15+15\cdot14\)

\(=15\cdot100=1500\)

c: \(93\cdot32+14\cdot16\)

\(=93\cdot32+32\cdot7\)

=3200

85.12,7 + 5.3.12,7

      = 12,7.(85 + 5.3)

      = 12,7. ( 85 + 15)

      = 12,7.100 = 1270

\(\text{∘ Ans}\)

\(\downarrow\)

`1,`

`86.15 + 150. 1,4`

`= 86. 15 + 15. 14`

`= 15.(86 + 14)`

`= 15.100`

`= 1500`

`2,`

`93.32 + 14.16`

`= 93.32 + 2.7.16`

`= 93.32 + 32.7`

`= 32.(93 + 7)`

`= 32.100`

`= 3200`

`3,`

\(98,6\cdot199-990\cdot9,86\)

`=`\(98,6\cdot199-99\cdot98,6\)

`=`\(98,6\cdot\left(199-99\right)\)

`=`\(98,6\cdot100\)

`=`\(9860\)

`4,`

\(85\cdot12,7+5\cdot3\cdot12,7?\)

`=`\(85\cdot12,7+15+12,7\)

`=`\(12,7\cdot\left(85+15\right)\)

`=`\(12,7\cdot100\)

`= 1270`

`5,`

\(0,12\cdot90-110\cdot0,6+36-25\cdot6?\)

\(=6\cdot1,8-11\cdot6+6\cdot6-25\cdot6\)

\(=6\cdot\left(1,8-11+6-25\right)\)

\(=6\cdot\left(-28,2\right)=-169,2\)

a) 85.12,7+5,3.12,7

=12,7(85+5,3)=1146,81

b) 52.143-52.39-8.26

=52.(143-39)-208

= 5200

=

85.12,7+5.3.12,7=12,7.(85+5.3)=12,7.(85+15)=12,7.100=1270

tính nhanh .

a)  85 .12,7 + 5.3.12,7 = 12,7 . ( 85 + 5.3 ) = 12,7 . (85+15) = 12,7 . 100 = 1270

b)  52.143 - 52.39 - 8.26 = 52.143 - 52.39 - 4.2.26 = 52.143 - 52.39 - 4.52 = 52.( 143 -39 - 4 ) = 52 . 100 = 5200

phân tích :

5x - 20y = 5 .(x - 4y)

5x(x-1)-3x.(x-1) = (x-1).(5x-3x) = 2x(x-1)  hoặc 5x(x-1)-3x(x-1) = x(x-1)(5-3) = 2x(x-1)

x.(x+y)-5x-5y = x(x+y) - 5 (x+y) = (x+y)(x-5)

85.12,7+5.3 .12,7                                 

= (85+5.3.)12,7

= 100 . 12,7

=1270

52.143-52.39-8.26

=52 . 143 - 52 . 39 - 4 . 2 . 26 
= 52 . 143 - 52 . 39 - 52 . 4 
= 52 . ( 143 - 39 - 4) 
= 52 . 100 
= 5200

a, 36.28+36.82 +64.69+64.41

=36(28+82)+64(69+41)

=36.110+64.110

=110(36+64)

=110.100

=11000

Hơi mờ

Câu 2 không biết làm

a) \(26^2+52.24+24^2=26^2+2.26.24+24^2\)

= \(\left(26+24\right)^2=50^2=2500\)

b) \(52^2+47^2+94.52\) ( câu này sai đề sửa luôn)

= \(52^2+2.47.52+47^2=\left(52+47\right)^2=99^2\)

= \(9801\)

c) \(50^2-49^2+48^2-47^2+...+2^2-1^2\)

= \(\left(50-49\right)\left(50+49\right)+\left(48-47\right)\left(48+47\right)+...+\left(2-1\right)\left(2+1\right)\)

= \(99+95+...+3\)

Dãy số này có : \(\dfrac{99-3}{4}+1=\dfrac{96}{4}+1=25\) số hạng

\(\Rightarrow\) \(99+95+...+3\) = \(\left(99+3\right).25:2=1275\)

d) \(87^2+26.87+13^2=87^2+2.13.87+13^2\)

\(=\left(87+13\right)^2=100^2=10000\)

e) \(3003^2-3^2=\left(3003-3\right)\left(3003+3\right)\)

= \(3000.3006=9018000\)

\(a,26^2+52\cdot24+24^2\\ =26^2+2\cdot26\cdot24+24^2\\ =\left(26+24\right)^2\\ =50^2\\ =2500\)

\(b,53^2+47^2+94\cdot53\\ =53^2+2\cdot47\cdot53+47^2\\ =\left(53+47\right)^2\\ =100^2\\ =10000\)

\(c,50^2-49^2+48^2-47^2+...+2^2-1^2\\ =\left(50+49\right)\left(50-49\right)+\left(48+47\right)\left(48-47\right)+...+\left(2+1\right)\left(2-1\right)\\ =99\cdot1+97\cdot1+...+3\cdot1\\ =99+97+...+3\\ \)

\(99+97+...+3\) có số số hạng là \(\dfrac{99-3}{2}+1=49\)(số)

\(\Rightarrow99+97+...+3=\dfrac{\left(99+3\right)\cdot49}{2}=2499\)

\(d,87^2+26\cdot87+13^2\\ =87^2+2\cdot13\cdot87+13^2\\ =\left(87+13\right)^2\\ =100^2\\ =10000\)

\(e,3003^2-3^2\\ =\left(3003+3\right)\left(3003-3\right)\\ =3006\cdot3000\\ =9018000\)

\(f,85\cdot12,7+5\cdot3\cdot12,7\\ =85\cdot12,7+15\cdot12,7\\ =12,7\cdot\left(85+15\right)\\ =12,7\cdot100\\ =1270\)

\(\text{Chúc bạn học tốt}\)

Áp dụng hằng đẳng thức:

a) 26^2+ 2.26.24 +24^2

= ( 26+ 24)^2 = 2500

b) hình như sai đề. đúng thì kết quả là. (53+47)^2=10000