Bài 1:
a) \(2x^2y-4xy^2+6xy\)
\(=2xy\left(x-2y+3\right)\)
b) \(4x^8y^2-8x^2y^8+2x^4y\)
\(=2x^2y\cdot\left(2x^6y-4y^7+x^2\right)\)
Bài 2:
a) \(4x^2-12x+9\)
\(=\left(2x-3\right)^2\)
b) \(4x^2+4x+1\)
\(=\left(2x+1\right)^2\)
c) \(1+12x+36x^2\)
\(=\left(1+6x\right)^2\)
Bài 3:
a) \(\left(3x-1\right)^2-16\)
\(=\left(3x-1-4\right)\left(3x-1+4\right)\)
\(=\left(3x-5\right)\left(3x+3\right)\)
b) \(\left(5x-4\right)^2-49x^2\)
\(=\left(5x-4-7x\right)\left(5x-4+7x\right)\)
\(=\left(-2x-4\right)\left(12x-4\right)\)
c) \(\left(2x+5\right)^2-\left(x-9\right)^2\)
\(=\left(2x+5-x+9\right)\left(2x+5+x-9\right)\)
\(=\left(x+14\right)\left(3x-4\right)\)
Bài 1:
\(a,2x^2y-4xy^2+6xy\\ =2xy\left(x-2y+3\right)\\ b,4x^3y^2-8x^2y^3+2x^4y\\ =2x^2y\left(2xy-4y^2+x^2\right)\)
Bài 2:
\(a,4x^2-12x+9\\ =\left(2x-3\right)^2\\ b,4x^2+4x+1\\ =\left(2x+1\right)^2\\ c,1+12x+36x^2\\ =\left(6x+1\right)^2\)
Bài 3:
\(a,\left(3x-1\right)^2-16\\ =\left(3x-5\right)\left(3x+3\right)\\=3\left(3x-5\right)\left(x+1\right)\\ b,\left(5x-4\right)^2-49x^2\\ =\left(-2x-4\right)\left(12x-4\right)\\ =-8\left(x+2\right)\left(3x-1\right)\\ c,\left(2x+5\right)^2-\left(x-9\right)^2\\ =\left(x+14\right)\left(3x-4\right)\)
Bài 4:
\(a,8x^3-64\\ =\left(2x-4\right)\left(4x^2+8x+16\right)\\ =8\left(x-2\right)\left(x^2+2x+4\right)\\ b,1+8x^3y^3\\ =\left(2xy+1\right)\left(4x^2y^2-2xy+1\right)\\ c,125x^3+1\\ =\left(5x+1\right)\left(25x^2-5x+1\right)\)
Bài 1:
a) \(2x^2y-4xy^2+6xy\)
⇔ \(2xy\left(x-2y+3\right)\)
b) \(4x^3y^2-8x^2y^3+2x^4y\)
⇔ \(2x^2y\left(2xy-4y^2+x^2y\right)\)
Bài 2:
a) \(4x^2-12x+9\)
⇔ \(\left(2x\right)^2-2\cdot2x\cdot3+3^3\)
⇔ \(\left(2x-3\right)^2\)
b) \(4x^2+4x+1\)
⇔ \(\left(2x\right)^2-2\cdot2x\cdot1+1^2\)
⇔ \(\left(2x-1\right)^2\)
c) \(1+12x+36x^2\)
⇔ \(1^2+2\cdot1\cdot6x+\left(6x\right)^2\)
⇔ \(\left(1+6x\right)^2\)
Bài 3:
a) \(\left(3x-1\right)^2-16\)
⇔ \(\left(3x-1\right)^2-4^2\)
⇔ \(\left(3x-1-4\right)\left(3x-1+4\right)\)
b) \(\left(5x-4\right)^2-49x^2\)
⇔ \(\left(5x-4\right)^2-\left(7x\right)^2\)
⇔ \(\left(5x-4-7x\right)\left(5x-4+7x\right)\)
c) \(\left(2x+5\right)^2-\left(x-9\right)^2\)
⇔ \(\left(2x+5-x+9\right)\left(2x+5+x-9\right)\)
Bài 4:
a) \(8x^3-64\)
⇔ \(\left(2x\right)^3-4^3\)
⇔ \(\left(2x-4\right)\left[\left(2x\right)^2+2x\cdot4+4^2\right]\)
b) \(1+8x^6y^8\)
⇔ \(1^3+\left(2x^3y^5\right)^3\)
⇔ \(\left(1+2x^3y^5\right)\left[1^3-1\cdot2x^3y^5+\left(2x^3y^5\right)^2\right]\)
c) \(125x^3+1\)
⇔ \(\left(5x\right)^3+1^3\)
⇔ \(\left(5x+1\right)\left[\left(5x\right)^2-5x\cdot1+1^2\right]\)
