rút gọn biểu thức sau: A = 8 x 4 x 125 x 25 + 96524 + 476 / 10 X 125 X 4 X 25 X 8
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Bài 9:
a) Ta có: \(A=\left(2x+y\right)^2-\left(2x+y\right)\left(2x-y\right)+y\left(x-y\right)\)
\(=4x^2+4xy+y^2-4x^2+y^2-xy-y^2\)
\(=3xy-y^2\)
\(=3\cdot\left(-2\right)\cdot3-3^2=-18-9=-27\)
b) Ta có: \(B=\left(a-3b\right)^2-\left(a+3b\right)^2-\left(a-1\right)\left(b-2\right)\)
\(=a^2-6ab+9b^2-a^2-6ab-9b^2-ab+2a+b-2\)
\(=-13ab+2a+b-2\)
\(=-13\cdot\dfrac{1}{2}\cdot\left(-3\right)+2\cdot\dfrac{1}{2}+\left(-3\right)-2\)
\(=\dfrac{31}{2}\)
Bài 7:
a) \(498^2=\left(500-2\right)^2=250000-2000+4=248004\)
b) \(93\cdot107=100^2-7^2=10000-49=9951\)
c) \(163^2+74\cdot163+37^2=\left(163+37\right)^2=200^2=40000\)
d) \(1995^2-1994\cdot1996=1995^2-1995^2+1=1\)
e) \(9^8\cdot2^8-\left(18^4-1\right)\left(18^4+1\right)\)
\(=18^8-18^8+1=1\)
f) \(125^2-2\cdot125\cdot25+25^2=\left(125-25\right)^2=100^2=10000\)
a, 410. 230=220.230=250
b,925.274.813= 350.312.312=374
Tương tự các câu khác....
a, 410.230 = (22)10.230 = 220.230 = 250
b, 925.274.813 = (32)25.(33)4.(34)3 = 350.312.312 = 374
c, 2550.1255 = (52)50.(53)5 = 5100.515 = 5115
d, 643.48.164 = (26)3.(22)8.(24)4 = 218.216.216 = 250
e, 38 : 36 = 32
210 : 83 = 210 : (23)3 = 210 : 29 = 2
127 : 67 = (12 : 6)7 = 27
@Dương Tuyết Mai
4 × 125 × 25 × 8
= (4 × 25) × (125 × 8)
= 100 × 1000
= 100 000
2 × 8 × 50 × 25 × 125
= (2 × 50) × (8 × 125) × 25
= 100 × 1000 × 125
= 12 500 000
2 × 3 × 4 × 5 × 50 × 25
= (2 × 50) × (4 × 25) × (3 × 5)
= 100 × 100 × 15
= 150 000
25 × 20 × 125 × 8 - 8 × 20 × 5 × 125
= 8 × 125 × 20 × (25 - 5)
= 1000 × 20 × 20
= 400 000
- (25 x 4) x (125 x8)=100 x 1000 =100000
- (50 x 2) x (8 x 125) x 25=100 x 1000 x 25 =2500000
- (2 x 50 ) x (4 x 25) x (3 x5)=100 x 100 x 15=150000
- 25 x 20 x125 x 8 - 5
= (20 x 5) x (125 x 8) -25=100 x 1000 -5 =100000 - 5 =99995
a) 25x² - 16
= (5x)² - 4²
= (5x - 4)(5x + 4)
b) 16a² - 9b²
= (4a)² - (3b)²
= (4a - 3b)(4a + 3b)
c) 8x³ + 1
= (2x)³ + 1³
= (2x + 1)(4x² - 2x + 1)
d) 125x³ + 27y³
= (5x)³ + (3y)³
= (5x + 3y)(25x² - 15xy + 9y²)
e) 8x³ - 125
= (2x)³ - 5³
= (2x - 5)(4x² + 10x + 25)
g) 27x³ - y³
= (3x)³ - y³
= (3x - y)(9x² + 3xy + y²)
a) \(25x^2-16=\left(5x-4\right)\left(5x+4\right)\)
b) \(16a^2-9b^2=\left(4a-3b\right)\left(4a+3b\right)\)
c) \(8x^3+1=\left(2x+1\right)\left(4x^2-2x+1\right)\)
d) \(125x^3+27y^3=\left(5x+3y\right)\left(25x^2-15xy+9y^2\right)\)
e) \(8x^3-125=\left(2x-5\right)\left(4x^2-10x+25\right)\)
g) \(27x^3-y^3=\left(3x-y\right)\left(9x^2+3xy+y^2\right)\)
222 x 5 = 111 x 2 x 5 = 1110
Đúng hay sai
3 x 125 x 2 x 8 = (3 x2 ) x (125 x 8) = 6000
Đúng hay sai
342 x 5 = 340 + 2 x 5 = 340 x 10 = 3400
Đúng hay sai
25 x 8 x 9 = (25 x 4) x (4 x 9) = 100 x 36 = 3600
Đúng hay sai
1 : Tính nhanh:
a) 2376 + 3425 - 376 - 425 = ( 2376 - 376 ) + ( 3425 - 425 )
= 2000 + 3000
= 5000
b)4638 - 2437 + 5362 - 7563 = 2210 + ( - 2210 )
= 0
c) 45 + 45 + 45 + 45 + 15 + 15 + 15 + 15
= 45 x 4 + 15 x 4
= ( 45 + 15 ) x 4
= 60 x 4
= 240
d) 4 x 125 x 25 x 8 = ( 4 x 25 ) x ( 125 x 8 )
= 100 x 1000
= 100000
e) 2 x 8 x 50 x 25 x 125 = ( 2 x 50 ) x ( 8 x 125 ) x 25
= 100 x 1000 x 25
= 100000 x 25
= 2500000
2 : Tính nhanh bằng 2 cách:
C1 : 125 + 125 + 125 + 125 - 25 - 25 - 25 - 25
= ( 125 - 25 ) + ( 125 - 25) + ( 125 - 25 ) + ( 125 - 25 )
=100 + 100 + 100 + 100
= 100 x 4
= 400
C2 : 125 + 125 + 125 + 125 - 25 - 25 - 25 - 25
= 125 x 4 - 25 x 4
= ( 125 - 25 ) x 4
= 100 x 4
= 400
\(A=\frac{8.4.125.25+96524+476}{10.125.4.25.8}\)
\(A=\frac{1000.100+96524+476}{10.1000.100}\)
\(A=\frac{100000+96524+476}{1000000}\)
\(A=\frac{100000+97000}{1000000}=\frac{197000}{1000000}=\frac{197}{1000}\)
\(A=0,197\)
A = 100000 + 96524 + 4760000
A = 4956524