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Dài 166
b) 2x2+3x-27=2x2-6x+9x-27=2x(x-3)+9(x-3)=(x-3)(2x+9)
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a) 16x2-(x2+4)2= (4x)2-(x2+4)2
= (4x-x2-4)(4x+x2+4)
\(\text{b) 27x^3-54x^2+36x-8=[(3x)^3-3.(3x)^2.2+3.3x.2^2-2^3}]\)
= (3x-2)3
\(\text{c) (x+y)^3 - (x-y)^3= (x+y-x+y)[(x+y)^2+(x+y)(x-y)+(x-y)^2]}\)
=2y(x2+2xy+y2+x2-y2+x2-2xy+y2)
= 2y(3x2+y2)
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a) \(-y^2+\dfrac{1}{9}\)
\(=-\left(y^2-\left(\dfrac{1}{3}\right)^2\right)\)
\(=-\left(y+\dfrac{1}{3}\right)\left(y-\dfrac{1}{3}\right)\)
b) \(4^4-256\)
\(=4^4-4^4\)
\(=0\)
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1)P\(=9\left(x+3\right)^2-4\left(x-2\right)^2\)\(=\left(3x+9\right)^2-\left(2x-4\right)^2\)
\(=\left(3x+9+2x-4\right)\left(3x+9-2x+4\right)\)(hằng đẳng thức số 3)
\(=\left(5x+5\right)\left(x+13\right)\)
\(=5\left(x+1\right)\left(x+13\right)\)
2)P\(=25\left(2x-y\right)^2-16\left(x+2y\right)^2\)\(=\left(10x-5y\right)^2-\left(4x+8y\right)^2\)
\(=\left(14x+3y\right)\left(6x-13y\right)\)(tương tự câu 1)
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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,\(x^3+9x^2+27x+27\)
\(\Leftrightarrow x^3+3.x^2.3+3x.9+3^3\)
\(\Leftrightarrow x^3+3x^2.3+3x+3^2+3^3\)
\(\Leftrightarrow\left(x+3\right)^3\)
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(x2 - 3)2 + 16
= (x2 - 3)2 + 42
= (x2 - 3 + 4)(x2 - 3 - 4)
= (x2 + 1)(x2 - 7)
đúng đi rồi làm cho