a: \(\left(2x-1\right)^2-2\left(2x-3\right)^2+4\)

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

\(=4x^2-4x+5-8x^2+24x-18\)

\(=-4x^2+20x-13\)

e: \(\left(2x+3y\right)\left(4x^2-6xy+9y^2\right)=8x^3+27y^3\)

a: Ta có: \(\left(2x-1\right)^2-2\left(2x-3\right)^2+4\)

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

\(=4x^2-4x+5-8x^2+24x-18\)

\(=-4x^2+20x-13\)

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

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

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

b) \(\left(4x^2+4xy+y^2\right):\left(2x+y\right)=\dfrac{\left(2x+y\right)^2}{2x+y}=2x+y\)

c) \(\left(x^2-6xy+9y^2\right):\left(3y-x\right)=\dfrac{\left(3y-x\right)^2}{3y-x}=3y-x\)

1b.=2((x+y)+(x+y)(x-y)+(x-y))=2(x²-y²+x+y+x-y)=2(x²-y²+2x)=2x²-2y²+4x

2a.=4xy+4xy+2y=8xy+2y=2y(4x+1)

b.=(3x)²+2.3x.y+y²-(2z)²=(3x+y)²-(2z)²=(3x+y-2z)(3x+y+2z)

c.=x²-x-7x+7=x(x-1)-7(x-1)=(x-1)(x-7)

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

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

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

\(=4x^2\)

hk tốt

^^

Bài 6a) x^3 - 8

c) x^3 - 27y^3

d) = x^6 - 27

Bài 5a) 6859

b) 8120601

\(5,\\ a,19^3=\left(20-1\right)^3=8000-3\cdot400\cdot1+3\cdot20\cdot1-1\\ =8000-1200+60-1=6859\\ b,201^3=\left(200+1\right)^3=8000000+3\cdot40000\cdot1+3\cdot200\cdot1+1\\ =8000000+120000+600+1=8120601\)

a: \(\left(\dfrac{1}{3}x+2y\right)\left(\dfrac{1}{9}x^2-\dfrac{2}{3}xy+4y^2\right)=\dfrac{1}{27}x^3+8y^3\)

b: \(\left(x^2-\dfrac{1}{3}\right)\left(x^4+\dfrac{1}{3}x^2+\dfrac{1}{9}\right)=x^6-\dfrac{1}{27}\)

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

\(A=x^3-8-128-x^3=-136\\ B=8x^3+27y^3-27x^3+8y^3=-19x^3+35y^3\)

\(A=\left(x-2\right)\left(x^2+2x+4\right)-\left(128+x^3\right)=x^3-8-128-x^3=-136\)

\(B=\left(2x+3y\right)\left(4x^2-6xy+9y^2\right)-\left(3x-2y\right)\left(9x^2+6xy+4y^2\right)=8x^3+27y^3-27x^3+8y^3=-19x^3+35y^3\)

\(A=x^3+2x^2+4x-2x^2-4x-8-128-x^3\)
\(A=-136\)
\(B=\left(2x+3y\right)\left(2x-3y\right)^2-\left(3x-2y\right)\left(3x+2y\right)^2\)
\(B=\left(2x+3y\right)\left(2x-3y\right)\left(2x-3y\right)-\left(3x-2y\right)\left(3x+2y\right)\left(3x+2y\right)\)
\(B=\left(4x^2-9y^2\right)\left(2x-3y\right)-\left(9x^2-4y^2\right)\left(3x+2y\right)\)
\(B=8x^3-12x^2y-18xy^2-27y^3-27x^3-18x^2y+12xy^2+8y^3\)
\(B=-19x^3-30x^2y-6xy^2-19y^3\)
\(B=-19\left(x^3-y^3\right)-6xy\left(5x+y\right)\)

a) \(\left(2x+3y\right)^2=\left(2x\right)^2+2\cdot2x\cdot3y+\left(3y\right)^2=4x^2+12xy+9y^2\)

b) \(\left(x+\dfrac{1}{4}\right)^2=x^2+2\cdot x\cdot\dfrac{1}{4}+\left(\dfrac{1}{4}\right)^2=x^2+\dfrac{1}{2}x+\dfrac{1}{16}\)

c) \(\left(x^2+\dfrac{2}{5}y\right)\left(x^2-\dfrac{2}{5}y\right)=\left(x^2\right)^2-\left(\dfrac{2}{5}y\right)^2=x^4-\dfrac{4}{25}y^2\)

d) \(\left(2x+y^2\right)^3=\left(2x\right)^3+3\cdot\left(2x\right)^2\cdot y^2+3\cdot2x\cdot\left(y^2\right)^2+\left(y^2\right)^3=8x^3+12x^2y^2+6xy^4+y^6\)

e) \(\left(3x^2-2y\right)^2=\left(3x^2\right)^2-2\cdot3x^2\cdot2y+\left(2y\right)^2=9x^4-12x^2y+4y^2\)

f) \(\left(x+4\right)\left(x^2-4x+16\right)=x^3+4^3=x^3+64\)

g) \(\left(x^2-\dfrac{1}{3}\right)\cdot\left(x^4+\dfrac{1}{3}x^2+\dfrac{1}{9}\right)=\left(x^2\right)^3-\left(\dfrac{1}{3}\right)^3=x^6-\dfrac{1}{27}\)