Tính nhanh:

a, 35x18 -5.7x28 = 35x18 -35x28 = 35 x (18 – 28) = 35 x ( -10) = -350

b,24x(16-5)-16x(24-5) = 24x16 – 24 x 5- 16x24 + 16x5 = (– 24 + 16)x 5 = -8 x 5 = -40

d,31x(-18)+31x(-81)-31 = 31x (-18  -81 – 1) =  31 x (-100) = -3100

e,(-12)x47+(-12)x52+(-12) = (-12)x (47+52 + 1)= (-12)x 100= - 1200

Ý c chưa rõ đề bài...

\(a.35\times18-5.7\times28\)

\(=35.18-35.28\)

\(=35.\left(18-28\right)\)

\(=35.\left(-10\right)\)

\(=-350\)

\(b.24.\left(16-5\right)-16.\left(24-5\right)\)

\(=24.16-24.5-16.24-16.5\)

\(=\left(24.16-16.24\right)-24.5-16.5\)

\(=0-\left(24+16\right).5\)

\(=0-40.5\)

\(=0-200\)

\(=-200\)

Ôi sr bn, câu b tớ nhầm dấu

`P = 24 . ( 31 + 14 ) - 31 . ( 24 - 14 )`

`P = 24 . 31 + 24 . 14 - 31 . 24 + 31 . 14`

`P = ( 24 . 31 - 31 . 24 ) + ( 24 . 14 + 31 . 14 )`

`P = 14 ( 24 + 31 )`

`P = 14 . 55 = 770`

P= 24.(31+14)-31.(24-14)

P=24.45-31.10

P=1080-310

P=770

b) Tại x=14 thì:\(B\left(x\right)=x^5-15x^4+16x^3-29x^2+13x\)

\(=x^5-\left(x+1\right)x^4+\left(x+2\right)x^3-\left(2x+1\right)x^2+x\left(x-1\right)\)

\(=x^5-x^5-x^4+x^4+2x^3-2x^3-x^2+x^2-x=-x=-14\)

a) A(x)=1

cậu giúp mình nốt phần kia đc k cậu

\(C=12+22+32+...+992+1002\)

\(=1+2\left(1+1\right)+3\left(2+1\right)+...+99\left(98+1\right)+100\left(99+1\right)\)

\(=1+1.2+2+2.3+3+...+98.99+99+99.100+100\)

\(=\left(1.2+2.3+3.4+...+99.100\right)+\left(1+2+3+...+99+100\right)\)\(=333300+5050=338350\)

a, \(A=x^3-30x^2-31x+1\)

\(=x^3-31x^2+x^2-31x+1\)

\(=x^2\left(x-31\right)+x\left(x-31\right)+1\)

\(=\left(x^2+x\right)\left(x-31\right)+1\)

Thay x = 31 \(\Rightarrow A=1\)

Vậy A = 1 khi x = 31

b, tách ra làm tương tự phần a

a,\(=x^3+x^2-\left(31x^2+31x\right)\)

\(=x^2\left(x+1\right)-31x\left(x+1\right)\)

\(=\left(x^2-31x\right)\left(x+1\right)=\left(31^2-31^2\right)\left(31+1\right)=0\)

b, Phân tích 3 số hạng đầu ta có:\(=x^5-x^4-\left(14x^4-14x^3\right)=\left(x^4-14x^3\right)\left(x-1\right)=\left(14^4-14^4\right)\left(x-1\right)=0\)

Thay x= 14 vào ta có: \(-29.14^2+13.14=-5502\)

c, do x=9 => x+1=10; Thay vào ta có:

\(C=x^{14}-\left(x+1\right)x^{13}+\left(x+1\right)x^{12}-...+\left(x+1\right)x^2-\left(x+1\right)x+10\)

\(C=x^{14}-x^{14}-x^{13}+x^{13}+x^{12}-....+x^3+x^2-x^2-x+10\)

\(C=-x+10=-9+10=1\)

CHÚC BẠN HỌC TỐT.....

a)    Ta có : \(x=31\Rightarrow30=x-1\)

Thay vào biểu thức ta được:

\(A=x^3-\left(x-1\right).x^2-x^2+1=x^3-x^3+x^2-x^2+1=1\)

b) Ta có: \(x=9\Rightarrow x+1=10\)

Thay vào biểu thức ta được

\(B=x^{14}-\left(x+1\right).x^{13}+\left(x+1\right).x^{12}-\left(x+1\right).x^{11}+.....+x^2.\left(x+1\right)=\left(x+1\right).x+\left(x+1\right)\)

\(\Leftrightarrow B=x^{14}-x^{14}-x^{13}+x^{13}+....+x^3+x^2=x^2+2x+1\)

\(\Leftrightarrow B=x^2-x^2-2x-1=-2.9-1=-19\)

\(x^{14}-10x^{13}+10x^{12}-10x^{11}+...+10x^2-10x+10\)

\(=x^{14}-\left(x+1\right)x^{13}+\left(x+1\right)x^{12}-\left(x+1\right)x^{11}+..+\left(x+1\right)x^2-\left(x+1\right)x+x+1\)

\(=x^{14}-x^{14}-x^{13}+x^{13}+x^{12}-x^{12}-x^{11}+...+x^3+x^2-x^2-x+x+1\)

\(=1\)

1. 14-24-12

= -10 - 12

= -10 + (-12)

= -22

2. (-25)+30-15

= 5-15

= -10

3. 13-31

= -18

CHÚC BẠN HỌC GIỎI

1. 14-24-12

=14+(-24)+(-12)

=[14+(-24)]+(-12)

=-10+(-12)

=-22

2. (-25)+30-15

=(-25)+30+(-15)

=[(-25)+(-15)]+30

=-40+30=-10

3. 13+31=-18

1)-22

2)-10

3)-18