Question

cần gấp

Answer 1

Bài 1:

a: \(\left(2x+y^2\right)^3\)

\(=\left(2x\right)^3+3\cdot\left(2x\right)^2\cdot y^2+3\cdot2x\cdot\left(y^2\right)^2+\left(y^2\right)^3\)

\(=8x^3+12x^2y^2+6xy^4+y^6\)

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

\(=\left(3x^2\right)^3+3\cdot\left(3x^2\right)^2\cdot2y+3\cdot3x^2\cdot\left(2y\right)^2+\left(2y\right)^3\)

\(=27x^6+54x^4y+36x^2y^2+8y^3\)

c: \(\left(\frac12x-3\right)^3\)

\(=\left(\frac12x\right)^3-3\cdot\left(\frac12x\right)^2\cdot3+3\cdot\frac12x\cdot3^2-3^3\)

\(=\frac18x^3-\frac94x^2+\frac{27}{2}x-27\)

d: \(\left(3x-\frac13\right)^3\)

\(=\left(3x\right)^3-3\cdot\left(3x\right)^2\cdot\frac13+3\cdot3x\cdot\left(\frac13\right)^2-\left(\frac13\right)^3\)

\(=27x^3-9x^2+x-\frac{1}{27}\)

Bài 2:

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

\(=\left(-x\right)^3+3\cdot\left(-x\right)^2\cdot1+3\cdot\left(-x\right)\cdot1^2+1^3\)

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

b: \(8-12x+6x^2-x^3\)

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

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

c: \(27x^3+54x^2+36x+8\)

\(=\left(3x\right)^3+3\cdot\left(3x\right)^2\cdot2+3\cdot3x\cdot2^2+2^3\)

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

d: \(64x^3-144x^2y+108xy^2-27y^3\)

\(=\left(4x\right)^3-3\cdot\left(4x\right)^2\cdot3y+3\cdot4x\cdot\left(3y\right)^2-\left(3y\right)^3\)

\(=\left(4x-3y\right)^3\)