Question

  

Answer 1

Bài 2: 

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

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

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

d) \(\left(2x+y\right)^3=\left(2x\right)^3+3\cdot\left(2x\right)^2\cdot y+3\cdot2x\cdot y^2+y^3=8x^3+12x^2y+6xy^2+y^3\)

e) \(\left(3x+1\right)^3=\left(3x\right)^3+3\cdot\left(3x\right)^2\cdot1+3\cdot3x\cdot1^2+1^3=27x^3+27x^2+9x+1\)

Answer 2

Bài 1:

a) \(16-24x+9x^2=4^2-2\cdot4\cdot3x+\left(3x\right)^2=\left(4-3x\right)^2\)

b) \(4x^2+\dfrac{1}{4}+2x=\left(2x\right)^2+2\cdot2x\cdot\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2=\left(2x+\dfrac{1}{2}\right)^2\)

c) \(4a^2+4a+1=\left(2a\right)^2+2\cdot2\cdot a+1^2=\left(2a+1\right)^2\)

d) \(-x^2+2xy-y^2-\left(x^2-2xy+y^2\right)\)

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

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

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

Answer 3

2:

a: (2x+1)(2x-1)=4x^2-1

b: (2x+y)(2x-y)=(2x)^2-y^2=4x^2-y^2

c: (x+1)^3=x^3+3x^2+3x+1

d: (2x+y)^3

=(2x)^3+3*(2x)^2*y+3*2x*y^2+y^3

=8x^3+12x^2y+6xy^2+y^3

e: (3x+1)^3

=(3x)^3+3*(3x)^2+3*3x+1

=27x^3+27x^2+9x+1

3:

a: 36*44=(40-4)(40+4)=40^2-16=1584

b: 86^2-14^2=(86-14)(86+14)=100*72=7200

c: 82*78=(80-2)(80+2)=80^2-2^2=6400-4=6396

d: 87*93=(90-3)(90+3)=90^2-9=8091

e: 125^2-25^2=(125-25)(125+25)=150*100=15000

g: 98^2=(100-2)^2

=10000-400+4=9604