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A, m2-7m+12=m2-3m+12-4m=m(m-3)-4(m-3)=(m-4)(m-3)
B, 2x4-x3+27-54x=x3(2-x)-27(2-x)=(x3-27)(2-x)=(x-3)(x2+3x+9)(2-x)
a) m^2 -7m +12 = m^2 -3m -4m +12
=m(m -3)-4 (m- 3)
=(m-4)(m-3)
b) 2x^4-x^3 -54x+ 27
=(2m^4-x^3)- (54x - 27)
=x^3(2x-1)-27(2x-1)
=(x^3-27)(2x-1)
Lời giải:
$x^3-4x^2-12x+27$
$=(x^3+3x^2)-(7x^2+21x)+(9x+27)$
$=x^2(x+3)-7x(x+3)+9(x+3)$
$=(x+3)(x^2-7x+9)$
\(x^3-4x^2+12x-27\)
\(=x^3-3x^2-x^2+3x+9x-27\)
\(=x^2\left(x-3\right)-x\left(x-3\right)+9\left(x-3\right)\)
\(=\left(x-3\right)\left(x^2-x+9\right)\)
a, = 2 x 2 - 6x +9x - 27
=(x-3).2x +9.(x-3)
=(x-3).(2x+9)
b, = 2x2-6xy+xy -3y2
= 2x.(x-3y) +y.(x-3y)
= (x-3y).(2x+y)
(x2 - 3)2 + 16
= (x2 - 3)2 + 42
= (x2 - 3 + 4)(x2 - 3 - 4)
= (x2 + 1)(x2 - 7)
a, \(m^3+27\)
\(\Leftrightarrow m^3+3^3\)
\(\Leftrightarrow\left(m+3\right)\left(m^2-m.3+3^2\right)\)
\(\Leftrightarrow\left(m+3\right)\left(m^2-3m+9\right)\)
b,\(\frac{1}{27}+a^3\)
\(\Leftrightarrow\frac{1}{27}\left(1+27a^3\right)\)
\(\Leftrightarrow\frac{1}{27}.\left(1+3a\right)\left(1-3a+9a^2\right)\)
c,\(\left(a+b\right)^3-c^3\)
\(\Leftrightarrow\left(a+b-c\right)\left[\left(a+b\right)^2+\left(a+b\right)c+c^2\right]\)
\(\Leftrightarrow\left(a+b-c\right)\left(a^2+2ab+b^2+ac+bc+c^2\right)\)
d,\(x^9+1\)
\(\Leftrightarrow\left(x^3+1\right)\left(x^6-x^3+1\right)\)
\(\Leftrightarrow\left(x+1\right)\left(x^2-x+1\right)\left(x^6-x^3+1\right)\)
e,\(x^3+9x^2+27x+27\)
\(\Leftrightarrow x^3+3.x^2.3+3x.9+3^3\)
\(\Leftrightarrow x^3+3x^2.3+3x+3^2+3^3\)
\(\Leftrightarrow\left(x+3\right)^3\)