Question

giúp em giải bài này với ạ

\[ \text{VD5. Viết các đa thức sau dưới dạng các hằng đẳng thức đã học.} \]

a) \( x^3 + 12x^2 + 48x + 64 \)

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

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

d) \( 8x^3 - 12x^2y + 6xy^2 - y^3 \)

e) \( 8x^3 + 6x^2 + \frac{3}{2}x + \frac{1}{8} \)

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

g) \( 8x^3 + 36x^2y + 54xy^2 + 27y^3 \)

h) \( 1 - 9x + 27x^2 - 27x^3 \)

Answer 1

a: \(x^3+12x^2+48x+64\)

\(=x^3+3\cdot x^2\cdot4+3\cdot x\cdot4^2+4^3\)

\(=\left(x+4\right)^3\)

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

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

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

d: \(8x^3-12x^2y+6xy^2-y^3\)

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

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

e: \(8x^3+6x^2+\frac32x+\frac18\)

\(=\left(2x\right)^3+3\cdot\left(2x\right)^2\cdot\frac12+3\cdot2x\cdot\left(\frac12\right)^2+\left(\frac12\right)^3\)

\(=\left(2x+\frac12\right)^3\)

f: \(27x^6-54x^4y+36x^2y^2-8y^3\)

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

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

g: \(8x^3+36x^2y+54xy^2+27y^3\)

\(=\left(2x\right)^3+3\cdot\left(2x\right)^2\cdot3y+3\cdot2x\cdot\left(3y\right)^2+\left(3y\right)^3\)

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

h: \(1-9x+27x^2-27x^3\)

\(=1^3-3\cdot1^2\cdot3x+3\cdot1\cdot\left(3x\right)^2-\left(3x\right)^3=\left(1-3x\right)^3\)