a: \(x^4+4=x^4+4x^2+4-4x^2=\left(x^2+2-2x\right)\left(x^2+2+2x\right)\)

c: \(x^3-125=\left(x-5\right)\left(x^2+5x+25\right)\)

\(\dfrac{1}{8}x^3-64=\left(\dfrac{1}{2}x-4\right)\left(\dfrac{1}{4}x^2+2x+16\right)\)

d: \(=\left(2x+5y\right)^3\)

a) \(9.3^3.\frac{1}{81}.3^2=3^2.3^3.\frac{1}{3^4}.3^2=3^7.\frac{1}{3^4}=3^3\)

b) \(4.2^5:\left(2^3.\frac{1}{16}\right)=2^2.2^5:2^3:\frac{1}{16}=2^7:2^3.16=2^4.2^4=2^8\)

c) \(3^2.2^5.\left(\frac{2}{3}\right)^2=3^2.2^5.\frac{2^2}{3^2}=2^5.2^2=2^7\)

d) \(\left(\frac{1}{3}\right)^2.\frac{1}{3}.9^2=\left(\frac{1}{3}\right)^3.\left(3^2\right)^2=\frac{1^3}{3^3}.3^4=1^3.3=3^1\)

bài 2: n=6

a. (a² - b²)² - (a² + b²)²

= (a² - b² - a² - b²)(a² - b² + a² + b²)

= -2b² . 2a²

b. a⁶ - b⁶

<=> (a³)² - (b³)²

<=> (a³ - b³)(a³ + b³)

\(a,\left(a^2-b^2\right)^2-\left(a^2+b^2\right)^2\\ =a^4-2a^2b^2+b^4-a^4-2a^2b^2-b^4\\ =-4a^2b^2\)

\(b,a^6-b^6=a^2\left(a^3-b^3\right)=a^2\left(a-b\right)\left(a^2+ab+b^2\right)\)

\(c,-4x^2+9y^2=\left(3y-2x\right)\left(3y+2x\right)\\ d,\left(x+1\right)^3-\left(2-x\right)^3\\ =\left(x+1-2+x\right)\left[\left(x+1\right)^2+\left(x+1\right)\left(2-x\right)+\left(2-x\right)^2\right]\\ =\left(2x-1\right)\left(x^2+2x+1-x^2+x+2+x^2-4x+4\right)\\ =\left(2x-1\right)\left(x^2-x+7\right)\)

\(e,8+\left(4x-3\right)^3\\ =\left(8+4x-3\right)\left[64-8\left(4x-3\right)+\left(4x-3\right)^2\right]\\ =\left(4x+5\right)\left(64-32x+24+16x^2-24x+9\right)\\ =\left(4x+5\right)\left(16x^2-56x+97\right)\)

\(g,81-\left(9-x^2\right)^2\\ =\left(9-9+x^2\right)\left(9+9-x^2\right)\\ =x^2\left(18-x^2\right)\left[=x^2\left(\sqrt{18}-x\right)\left(\sqrt{18}+x\right)\right]\)

Chỗ trong ngoặc nếu bạn chưa học căn thì ko cần ghi nha

a: Ta có: \(\left(a^2-b^2\right)^2-\left(a^2+b^2\right)^2\)

\(=\left(a^2-b^2-a^2-b^2\right)\left(a^2-b^2+a^2+b^2\right)\)

\(=-4a^2b^2\)

b: \(a^6-b^6\)

\(=\left(a^3-b^3\right)\left(a^3+b^3\right)\)

\(=\left(a-b\right)\left(a+b\right)\left(a^2+ab+b^2\right)\left(a^2-ab+b^2\right)\)

d: \(\left(x+1\right)^3+\left(x-2\right)^3\)

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

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

\(=\left(2x-1\right)\left(x^2-x+7\right)\)

b: \(3^4\cdot3^5:\dfrac{1}{27}==3^9\cdot3^3=3^{12}\)

1) a) 4⁸.2²⁰ = (2²)⁸.2²⁰

= 2¹⁶.2²⁰ = 2³⁶

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9¹².27⁵.81³ = (3²)¹².(3³)⁵.(3⁴)⁴

= 3²⁴.3¹⁵.3¹⁶ = 3⁵⁵

--------

64³.4⁵.16² = (4³)³.4⁵.(4²)²

= 4⁹.4⁵.4⁴ = 4¹⁸

b) 25²⁰.125⁴ = (5²)²⁰.(5³)⁴

= 5⁴⁰.5¹² = 5⁵²

--------

x⁷.x³.x⁴ = x¹⁴

--------

3⁶.4⁶ = (3.4)⁶ = 12⁶

2) a) 2² = 4

2³ = 8

2⁴ = 16

2⁵ = 32

2⁶ = 64

2⁷ = 128

2⁸ = 256

2⁹ = 512

2¹⁰ = 1024

b) 3² = 9

3³ = 27

3⁴ = 81

3⁵ = 243

c) 4² = 16

4³ = 64

4⁴ = 256

d) 5² = 25

5³ = 125

5⁴ = 625

3)

a) 4⁹ : 4⁴ = 4⁵

17⁸ : 17⁵ = 17³

2¹⁰ : 8² = 2¹⁰ : (2³)² = 2¹⁰ : 2⁶ = 2⁴

18¹⁰ : 3¹⁰ = (18 : 3)¹⁰ = 6¹⁰

27⁵ : 81³ = (3³)⁵ : (3⁴)³ = 3¹⁵ : 3¹² = 3³

b) 10⁶ : 100 = 10⁶ : 10² = 10⁴

5⁹ : 25³ = 5⁹ : (5²)³ = 5⁹ : 5⁶ = 5³

4¹⁰ : 64³ = 4¹⁰ : (4³)³ = 4¹⁰ : 4⁹ = 4

2²⁵ : 32⁴ = 2²⁵ : (2⁵)⁴ = 2²⁵ : 2²⁰ = 2⁵

18⁴ : 9⁴ = (18 : 9)⁴ = 2⁴

a: \(\left(x+y+z\right)^2-\left(y+z\right)^2\)

\(=\left(x+y+z-y-z\right)\left(x+y+z+y+z\right)\)

\(=x\left(x+2y+3z\right)\)

b: \(\left(x+3\right)^2+4\left(x+3\right)+4\)

\(=\left(x+3+2\right)^2\)

\(=\left(x+5\right)\left(x+5\right)\)

c: \(25+10\left(x+1\right)+\left(x+1\right)^2\)

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

\(=\left(x+6\right)\left(x+6\right)\)

a) 9 . 3³ . 1/81 . 3²

=3².3³.1/3⁴.3²

=3³

b) 4 . 2⁵ : (2³ . 1/16)

=2².2⁵:(2³.1/2⁴)

=2².2⁵:1/2

=2².2⁴

=2²⁺⁴

=2⁶

c) 3² . 2⁵ . (2/3)²

=3².2⁵.2²/3²

=2⁵.2²

=2⁵⁺²

=2⁷

d) (1/3)² . 1/3 . 9²

=1/3².1/3.(3²)²

=1/3².1/3.3⁴

=1/3².3³

=3

=3¹

a) 3³

b) 2⁷

c) 3

a=3³

b=2⁷

c=3