\(x^3+6x^2y+12xy^2+8y^3\\=x^3+3\cdot x^2\cdot2y+3\cdot x\cdot(2y)^2+(2y)^3\\=(x+2y)^3\)

Trả lời:

Ta có: ( x - 2y )³ = x³ - 3.x².2y + 3.x.( 2y )² - ( 2y )³ = x³ - 6x²y + 12xy² - 8y³ ( HĐT thứ 5 - lập phương của 1 hiệu )

=> Chọn b

chọn đáp án đúng và giải thick ra nhé

\(12x-9-4x^2=-\left(2x-3\right)^2\\ Sửa:x^3-6x^2y+12xy^2-8y^3=\left(x-2y\right)^3\)

a

\(8x^3-\dfrac{1}{125}y^3\\ =\left(2x\right)^3-\left(\dfrac{1}{5}y\right)^3\\ =\left(2x-\dfrac{1}{5}y\right)\left[\left(2x\right)^2+2x.\dfrac{1}{5}y+\left(\dfrac{1}{5}y\right)^2\right]\\ =\left(2x-\dfrac{1}{5}y\right)\left(4x^2+\dfrac{2}{5}xy+\dfrac{1}{25}y^2\right)\)

b

\(-x^3+6x^2y-12xy^2+8y^3\\ =-\left(x^3-6x^2y+12xy^2-8y^3\right)\\ =-\left(x^3-3.2y.x^2+3.\left(2y\right)^2.x-\left(2y\right)^3\right)\\ =-\left(x-2y\right)^3\\ =-\left(x-2y\right)\left(x-2y\right)\left(x-2y\right)\)

a: 8x^3-1/125y^3

=(2x)^3-(1/5y)^3

=(2x-1/5y)(4x^2+2/5xy+1/25y^2)

b: =(2y-x)^3

a) \(8x^3-\dfrac{1}{125}y^3\)

\(=\left(2x\right)^3-\left(\dfrac{1}{5}y\right)^3\)

\(=\left(2x-\dfrac{1}{5}y\right)\left[\left(2x\right)^2+2x\cdot\dfrac{1}{5}y+\left(\dfrac{1}{5}y\right)^2\right]\)

\(=\left(2x-\dfrac{1}{5}y\right)\left(4x^2+\dfrac{2}{5}xy+\dfrac{1}{24}y^2\right)\)

b) \(-x^3+6x^2y-12xy^2+8y^3\)

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

\(=-\left(x^3-3\cdot x^2\cdot2y+3\cdot x\cdot\left(2y\right)^2-\left(2y\right)^3\right)\)

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

\(...=A=x^3-3x^2+3x-1+1013\)

\(A=\left(x-1\right)^3+1013=\left(11-1\right)^3+1013=1000+1013=2013\)

\(...B=x^3-6x^2+12x-8-100\)

\(B=\left(x-2\right)^3-100=\left(12-2\right)^3-100=1000-100=900\)

\(...C=\left(x-2y\right)^3=\left(-2y-2y\right)^3=\left(-4y\right)^3=-64y^3\)

\(...D=x^3+9x^2+27x+9+2018\)

\(D=\left(x+3\right)^3+2018=\left(-23+3\right)^3+2018=-8000+2018=-5982\)

a) \(A=x^3-3x^2+3x+1012\)

\(A=x^3-3\cdot x^2\cdot1+3\cdot x\cdot1^2-1+1013\)

\(A=\left(x-1\right)^3+1013\)

Thay x=11 vào A ta có:

\(A=\left(11-1\right)^3+1013=10^3+1013=1000+1013=2013\)

b) \(B=x^3-6x^2+12x-108\)

\(B=x^3-3\cdot2\cdot x^2+3\cdot2^2\cdot x-8-100\)

\(B=\left(x-2\right)^3-100\)

Thay x=12 vào B ta có:

\(B=\left(12-2\right)^3-100=10^3-100=1000-100=900\)

c) \(C=x^3+6x^2y+12xy^2+8y^3\)

\(C=x^3+3\cdot2y\cdot x^2+3\cdot\left(2y\right)^2\cdot x+\left(2y\right)^3\)

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

Thay x=-2y vào C ta được:

\(C=\left(-2y+2y\right)^3=0^3=0\)

d) \(D=x^3+9x^2+27x+2027\)

\(D=x^3+3\cdot3\cdot x^2+3\cdot3^2\cdot x+27+2000\)

\(D=\left(x+3\right)^3+2000\)

Thay x=-23 vào D ta có:

\(D=\left(-23+3\right)^3+2000=\left(-20\right)^3+2000=-8000+2000=-6000\)