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

a, \(x^4-8x^2+16=\left(x^2-4\right)^2\)

b, \(\left(4x+5\right)^2-\left(5x+4\right)^2=\left(4x+5-5x-4\right)\left(4x+5+5x+4\right)=\left(1-x\right)\left(9x+9\right)=9\left(1-x\right)\left(1+x\right)=9\left(1-x^2\right)\)

c, \(\left(2x-3\right)^2-2\left(2x-3\right)\left(x+2\right)+\left(-x-2\right)^2=\left(2x-3-x-2\right)^2=\left(x-5\right)^2\)

a) \(x^4-8x^2+16=\left(x^2-4\right)^2\)

b) \(\left(4x+5\right)^2-\left(5x+4\right)^2=\left(4x+5-5x-4\right)\left(4x+5+5x+4\right)=9\left(1-x\right)\left(x+1\right)\)c) \(\left(2x-3\right)^2-2.\left(2x-3\right)\left(x+2\right)+\left(-x-2\right)^2=\left(2x-3-x-2\right)^2=\left(x-5\right)^2\)

1a/ z² - 6z + 5 - t² - 4t = z² - 2 . 3z + 3² - 4 - t² - 4t = (z² - 2 . 3z + 3²) - (2² + 2 . 2t + t²) = (z - 3)² - (2 + t)²

b/ x² - 2xy + 2y² + 2y² + 1 = x² - 2xy + y² + y² + 2y + 1 = (x² - 2xy + y²) + (y² + 2y + 1) = (x - y)² + (y + 1)²

c/ 4x² - 12x - y² + 2y + 8 = (2x)² - 12x - y² + 2y + 3² - 1 = [ (2x)² - 2 . 3 . 2x + 3² ] - (y² - 2y + 1) = (2x - 3)² - (y - 1)²

2a/ (x + y + 4)(x + y - 4) = x² + xy - 4x + xy + y² - 4y + 4x + 4y + 16 = x² + (xy + xy) + (-4x + 4x) + (-4y + 4y) + y² + 16

= x² + 2xy + y² + 4² = (x + y)² + 4²

b/ (x - y + 6)(x + y - 6) = x² + xy - 6x - xy - y² + 6y + 6x + 6y - 36 = x² + (xy - xy) + (-6x + 6x) + (6y + 6y) - y² - 36

= x² - y² + 12y - 6² = x² - (y² - 12y + 6²) = x² - (y² - 2 . 6y + 6²) = x² - (y - 6)²

c/ (y + 2z - 3)(y - 2z - 3) = y² -2yz - 3y + 2yz - 4z² - 6z - 3y + 6z + 9 = y² + (-2yz + 2yz) + (-3y - 3y) + (-6z + 6z) - 4z² + 9

= y² - 6y - 4z² + 9 = (y² - 6y + 9) - 4z² = (y - 3)² - (2z)²

d/ (x + 2y + 3z)(2y + 3z - x) = 2xy + 3xz - x² + 4y² + 6yz - 2xy + 6yz + 9z² - 3xz = (2xy - 2xy) + (3xz - 3xz) - x² + (6yz + 6yz) + 9z² + 4y²

= -x² + 4y² + 12yz + 9z² = (4y² + 12yz + 9z²) - x² = [ (2y)² + 2 . 2 . 3yz + (3z)² ] - x² = (2y + 3z)² - x²

:v dễ mà có trong nâng cao mới hc qua :3

a, x2+10x+26+y2+2y

=(x2+2.x.5+52)+(12+2.1.y+y2)

=(x+5)2+(y+1)2

b, x2−2xy+2y2+2y+1

=x2−2xy+y2+y2+2y+1

=(x2−2.x.y+y2)+(y2+2.y.1+12)

=(x−y)2+(y+1)2

c,z2−6z+5−t2−4t

=−(t2+4t−z2+6z−5)

=−(t2+2.t.2+22−z2+2.z.3−32)

=−((t2+2.t.2+22)−(z2−2.z.3+32))

=−((t+2)2−(z−3)2)

=(z−3)2−(t+2)2

A

Chọn A

1. 

2.

 \(\begin{array}{l}\left( {3x - 2y} \right)\left( {9{x^2} + 6xy + 4{y^2}} \right) + 8{y^3}\\ = \left( {3x - 2y} \right)\left[ {{{\left( {3x} \right)}^2} + 3x.2y + {{\left( {2y} \right)}^2}} \right] + 8{y^3}\\ = {\left( {3x} \right)^3} - {\left( {2y} \right)^3} + 8{y^3}\\ = 27{x^3} - 8{y^3} + 8{y^3}\\ = 27{x^3}\end{array}\)

Bài 1:

a) \(x^2+10x+26+y^2+2y=(x^2+10x+25)+(y^2+2y+1)\)

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

b) \(z^2-6z+5-t^2-4t=(z^2-6t+9)-(t^2+4t+4)\)

............................................= \(\left(z-3\right)^2-\left(t+2\right)^2\)

c) \(x^2-2xy+2y^2+2y+1=(x^2-2xy+y^2)+(y^2+2y+1)\)

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

d) \(4x^2-12x-y^2+2y+8=\left(4x^2-12x+9\right)-\left(y^2-2y+1\right)\)

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

Bài 2:

a) \(\left(x+y+4\right)\left(x+y-4\right)=\left(x+y\right)^2-16\)

b) \(\left(x-y+6\right)\left(x+y-6\right)=x^2-\left(y-6\right)^2\)

c) \(\left(y+2z-3\right)\left(y-2z+3\right)=y^2-\left(2z-3\right)^2\)

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

a: \(=x^4+16x^2+81\)

\(=\left(x^2+9\right)^2-2x^2\)

\(=\left(x^2+9-x\sqrt{2}\right)\left(x^2+9+x\sqrt{2}\right)\)

b: \(=x^4+4x^2+4-4x^2\)

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

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

a: \(2^6\cdot3^3=\left(2^2\cdot3\right)^3=12^3\)

b: \(6^4\cdot8^3=2^4\cdot3^4\cdot2^9=2^{13}\cdot3^4\)

c: \(16\cdot81=36^2\)

d: \(25^4\cdot2^8=100^4\)

A = 2⁵.(-5)² - 8² - 7

= 32.25 - 64 - 7

= 729

= 27²

B = 2³.(-4)² + (-3)².3² - 40

= 8.16 + 9.9 - 40

= 169

= 13²

C = (1/4 - 1/2 - 1)³ . (2 - 2/5)³

= (-5/4)³ . (8/5)³

= (-5/4 . 8/5)³

= (-2)³

D = (-1/4)² : (1/2 - 1/3)

= 1/16 : 1/6

= 3/8

E = 4 . (1/4)² + 25 . [(3/4)³ : (5/4)³] : (3/2)³

= 1/4 + 25 . (3/4 . 5/4)³ : (3/2)³

= 1/4 + 25 . (15/16)³ : 27/8

= 1/4 + 25 . 3375/4096 : 27/8

= 1/4 + 84375/4096 : 27/8

= 1/4 + 3125/512

= 3253/512

F = 2³ + 3.(1/2)⁰ - 1 + [(-2)² : 1/2] - 8

= 8 + 3.1 - 1 + (4 : 1/2) - 8

= 8 + 3 - 1 + 8 - 8

= 10