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a: \(x^3+8=\left(x+2\right)\left(x^2-2x+4\right)\)
b: \(27-8y^3=\left(3-2y\right)\left(9+6y+4y^2\right)\)
c: \(y^6+1=\left(y^2+1\right)\left(y^4-y^2+1\right)\)
d: \(64x^3-\dfrac{1}{8}y^3=\left(4x-\dfrac{1}{2}y\right)\left(16x^2+2xy+\dfrac{1}{4}y^2\right)\)
D) 64x^3-1/8y^3
= (4x)^3 + (1/2y)^3
= ( 4x + 1/2y ) [ (4x)^2 - 4x.1/2y + (1/2y)^2 ]
E) 125x^6-27y^9
( câu này mik chưa rõ nên vx chưa tek giải cho bn )
HOk tốt nhé
\(a,=\left(3+x\right)\left(9-3x+x^2\right)\\ b,=\left(4x+0,1\right)\left(16x^2-0,4x+0,01\right)\\ c,=\left(2-3x\right)\left(4+6x+9x^2\right)\\ d,=\left(\dfrac{x}{5}-\dfrac{y}{3}\right)\left(\dfrac{x^2}{25}+\dfrac{xy}{15}+\dfrac{y^2}{9}\right)\)
Bài 1:
\(1,Sửa:x^3-2x^2+x=x\left(x^2-2x+1\right)=x\left(x-1\right)^2\\ 2,=6\left(x^2+2xy+y^2\right)=6\left(x+y\right)^2\\ 3,=2y\left(y^2+4y+4\right)=2y\left(y+2\right)^2\\ 4,=5\left(x^2-2xy+y^2\right)=5\left(x-y\right)^2\)
Bài 2:
\(1,=x\left(x^2-64\right)=x\left(x-8\right)\left(x+8\right)\\ 2,=2y\left(4x^2-9\right)=2y\left(2x-3\right)\left(2x+3\right)\\ 3,=3\left(x^3-1\right)=3\left(x-1\right)\left(x^2+x+1\right)\)
Bài 3:
\(a,=5\left(x^2+2x+1-y^2\right)=5\left[\left(x+1\right)^2-y^2\right]=5\left(x-y+1\right)\left(x+y+1\right)\\ b,=3x\left(x^2-2x+1-4y^2\right)=3x\left[\left(x-1\right)^2-4y^2\right]\\ =3x\left(x-2y-1\right)\left(x+2y-1\right)\\ c,=ab\left(a-b\right)\left(a+b\right)+\left(a+b\right)^2\\ =\left(a+b\right)\left(a^2b-ab^2+a+b\right)\\ d,=2x\left(x^2-y^2-4x+4\right)=2x\left[\left(x-2\right)^2-y^2\right]\\ =2x\left(x-y-2\right)\left(x+y-2\right)\)
1. x2 - 6x + 9=(x-3)2
2. 25 + 10x + x2=(x+5)2
3. \(\dfrac{1}{4}a^2+2ab^2+4b^4=\left(\dfrac{1}{2}a+2b^2\right)^2\)
4.\(\dfrac{1}{9}-\dfrac{2}{3}y^4+y^8=\left(\dfrac{1}{3}-y^4\right)^2\)
5.x3 + 8y3=(x+8y)(x2-8xy+64y2)
6.8y3 -125=(2y-5)(4y2+10y+25)
7.a6-b3=(a2-b)(a4+a2b+b2)
8 x2 - 10x + 25=(x-2)2
1) \(x^2-6x+9=\left(x-3\right)^2\)
2) \(25+10x+x^2=\left(5+x\right)^2\)
3) \(\dfrac{1}{4}a^2+2ab+4b^4=\left(\dfrac{1}{2}a+2b^2\right)^2\)
4) \(\dfrac{1}{9}-\dfrac{2}{3}y^4+y^8=\left(\dfrac{1}{3}-y^4\right)^2\)
5) \(x^3+8y^3=\left(x+2y\right)\left(x^2-2xy+4y^2\right)\)
6) \(8y^3-125=\left(2y-5\right)\left(4y^2+10y+25\right)\)
7) \(a^6-b^3=\left(a^2-b\right)\left(a^4+a^2b+b^2\right)\)
8) \(x^2-10x+25=\left(x-5\right)^2\)
9) \(8x^3-\dfrac{1}{8}=\left(2x-\dfrac{1}{2}\right)\left(4x^2+x+\dfrac{1}{4}\right)\)
a) x² - 9
= x² - 3²
= (x - 3)(x + 3)
b) 4x² - 1
= (2x)² - 1²
= (2x - 1)(2x + 1)
c) x⁴ - 16
= (x²)² - 4²
= (x² - 4)(x² + 4)
= (x² - 2²)(x² + 4)
= (x - 2)(x + 2)(x + 4)
d) x² - 4x + 4
= x² - 2.x.2 + 2²
= (x - 2)²
e) x³ - 8
= x³ - 2³
= (x - 2)(x² + 2x + 4)
f) x³ + 3x² + 3x + 1
= x³ + 3.x².1 + 3.x.1² + 1³
= (x + 1)³
a) \(x^3+8=x^3+2^3=\left(x+2\right)\left(x^2-2x+4\right)\)
b) \(27-8y^3=3^3-\left(2y\right)^3=\left(3-2y\right)\left(9+6y+4y^2\right)\)
c) \(y^6+1=\left(y^2\right)^3+1^3=\left(y^2+1\right)\left(y^4-y^2+1\right)\)