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\(27x^3-27x^2+18x-4=27x^3-9x^2-18x^2+6x+12x-4\)
\(=9x^2\left(3x-1\right)-6x\left(3x-1\right)+4\left(3x-1\right)\)
\(=\left(3x-1\right)\left(9x^2-6x+4\right)\)
\(a,M=27x^3+108x^2+144x+64=\left(3x+4\right)^2\)Tại \(x=32\Rightarrow M=\left(3.32+4\right)^3=100^3=1000000\)
\(b,N=27x^3-54x^2+36x-8=\left(3x-2\right)^3\)
Tại \(x=14\Rightarrow N=\left(3.14-2\right)^3=40^3=64000\)
\(27x^3-27x^2+18x-4\)
\(=27x^3-9x^2-18x^2+6x+12x-4\)
\(=\left(27x^3-9x^2\right)-\left(18x^2-6x\right)+\left(12x-4\right)\)
\(=9x^2.\left(3x-1\right)-6x\left(3x-1\right)+4\left(3x-1\right)\)
\(=\left(3x-1\right)\left(9x^2-6x+4\right)\)
\(27x^3-27x^2+18x-4\)
\(=27x^3-18x^2+12x-9x^2+6x-4\)
\(=3x\left(9x^2-6x+4\right)-\left(9x^2-6x+4\right)\)
\(=\left(3x-1\right)\left(9x^2-6x+4\right)\)
27x3 - 27x2 + 18x - 4
= 27x3 - 9x2 - 18x2 + 6x + 12x - 4
= 9x2 ( 3x - 1 ) - 6x ( 3x - 1 ) + 4 ( 3x - 1 )
= ( 9x2 - 6x + 4 ) ( 3x - 1 )
a) \(2x^3-x^2+5x+3\)
\(=2x^3-2x^2+x^2+6x-x+3\)
\(=\left(2x^3-2x^2+6x\right)+\left(x^2-x+3\right)\)
\(=2x\left(x^2-x+3\right)+\left(x^2-x+3\right)\)
\(=\left(2x+1\right)\left(x^2-x+3\right)\)
b) \(27x^3-27x^2+18x-4\)
\(=27x^3-18x^2-9x^2+12x+6x-4\)
\(=\left(27x^3-18x^2+12x\right)-\left(9x^2-6x+4\right)\)
\(=3x\left(9x^2-6x+4\right)-\left(9x^2-6x+4\right)\)
\(=\left(3x-1\right)\left(9x^2-6x+4\right)\)
27x3 + 108x2 + 114x + 64 = ( 3x )3 + 3.( 3x )2.4 + 3.3x.42 + 43 = ( 3x + 4 )3