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4 tháng 10 2021
1) \(\dfrac{1}{27}+a^3=\left(\dfrac{1}{3}+a\right)\left(\dfrac{1}{9}-\dfrac{a}{3}+a^2\right)\)
2) \(=\left(2x+3y\right)\left(4x^2-6xy+9y^2\right)\)
3) \(=\left(\dfrac{1}{2}x+2y\right)\left(\dfrac{1}{4}x-xy+4y^2\right)\)
4) \(=\left(x^2+1\right)\left(x^4-x^2+1\right)\)
5) \(=\left(x^3+1\right)\left(x^6-x^3+1\right)\)
6) \(=\left(x-4\right)\left(x^2+4x+16\right)\)
7) \(=\left(x-5\right)\left(x^2+5x+25\right)\)
8) \(=\left(2x^2-3y\right)\left(4x^4+6x^2y+9y^2\right)\)
9) \(=\left(\dfrac{1}{4}x^2-5y\right)\left(\dfrac{1}{16}x^4+\dfrac{5}{4}x^2y+25y^2\right)\)
10) \(=\left(\dfrac{1}{2}x-2\right)\left(\dfrac{1}{4}x^2+x+4\right)\)
11) \(=\left(x+2\right)^3\)
12) \(=\left(x+3\right)^3\)
12 tháng 1 2023
a: \(=\left(x+1+5\right)\left(x+1-5\right)=\left(x+6\right)\left(x-4\right)\)
b: =(1-2x)(1+2x)
c: \(=\left(2-3x\right)\left(4+6x+9x^2\right)\)
d: =(x+3)^3
e: \(=\left(2x-y\right)^3\)
f: =(x+2y)(x^2-2xy+4y^2)
7 tháng 9 2017
a) \(x^2\)\(+\)\(6x\)\(+\)\(9\)
\(=\left(x+3\right)^2\)
b) \(x^3\)\(+\)\(3x^2\)\(+\)\(3x\)\(+\)\(1\)
\(=\left(x+1\right)^3\)
c) \(8x^3\)\(-\)\(\frac{1}{8}\)
\(=\left(2x-\frac{1}{2}\right)\left(4x^2+x+\frac{1}{4}\right)\)
d) \(10x\)\(-\)\(25\)\(-\)\(x^2\)
\(=\)\(-x^2\)\(+\)\(10\)\(-\)\(25\)
\(=-\left(x^2-10+25\right)\)
\(=-\left(x-5\right)^2\)
e) \(\frac{1}{25}x^2\)\(-\)\(64y^2\)
=\(\left(\frac{1}{25}x-8y\right)\left(\frac{1}{5}x+8y\right)\)
NN
2
14 tháng 12 2017
1) \(27+27x+9x^2+x^3\)
\(=3^3+3.3^2.x+3.3.x^2+x^3\)
\(=\left(3+x\right)^3\)
2) \(8-27x^3\)
\(=2^3-\left(3x\right)^3\)
\(=\left(2-3x\right)\left[2^2+2.3x+\left(3x\right)^2\right]\)
\(=\left(2-3x\right)\left(4+6x+9x^2\right)\)
14 tháng 12 2017
\(1,27+27+9x^2+x^3\)
\(=\left(3+x\right)^3\)
\(2,8-27x^3\)
\(=\left(2-3x\right).\left(4+6x+9x^2\right)\)
\(3,x^{64}+x^{32}+1\)
\(=\left(x^{64}+2x^{32}+1\right)-x^{32}\)
\(=\left(x^{32}+1\right)^2-x^{32}\)
\(=\left(x^{32}+1-x^{16}\right).\left(x^{32}+1+x^{16}\right)\)
Công nhận câu 3 hơi căng~
\(x^3+1\)
\(=x^3+1^3\)
\(=\left(x+1\right)\left(x^2-x+1\right)\)
______
\(8+x^3\)
\(=2^3+x^3\)
\(=\left(2+x\right)\left(4-2x+x^2\right)\)
______
\(27x^3-64y^3\)
\(=\left(3x\right)^3-\left(4y\right)^3\)
\(=\left(3x-4y\right)\left(9x^2+12xy+16y^2\right)\)
______
\(\dfrac{x^3}{64}-\dfrac{1}{125}\)
\(=\left(\dfrac{x}{4}\right)^3-\left(\dfrac{1}{5}\right)^3\)
\(=\left(\dfrac{x}{4}-\dfrac{1}{5}\right)\left(\dfrac{x^2}{16}+\dfrac{x}{20}+\dfrac{1}{25}\right)\)
x^3+1=(x+1)(x^2-x+1)
x^3+8=(x+2)(x^2-2x+4)
27x^3-64y^3=(3x-4y)(9x^2+12xy+16y^2)
\(\dfrac{x^3}{64}-\dfrac{1}{25}=\left(\dfrac{1}{4}x-\sqrt[3]{\dfrac{1}{5}}\right)\left(\dfrac{1}{16}x^2+\dfrac{1}{4\sqrt[3]{5}}\cdot x+\dfrac{1}{\sqrt[3]{25}}\right)\)