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b,\(4x^3-4x^2-9x+9\)
\(=\left(4x^3-4x^2\right)+\left(-9x+9\right)\)
\(=4x^2\left(x-1\right)-9\left(x-1\right)\)
\(=\left(4x^2-9\right)\left(x-1\right)\)
c,\(xy-x^2+x-y\)
\(=\left(xy-y\right)+\left(-x^2+x\right)\)
\(=y\left(x-1\right)-x\left(x-1\right)\)
\(=\left(y-x\right)\left(x-1\right)\)
Câu a đề kì kì sao á.
\(4a^2-4a+1-b^2\)
=\(\left(4a^2-4a+1\right)-b^2\)
=\(\left(2a-1\right)^2-b^2\)
=\(\left(2a-1-b\right)\left(2a-1+b\right)\)
\(4x^3-4x^2-9x+9\)
=\(\left(4x^3-4x^2\right)-\left(9x-9\right)\)
=\(4x^2\left(x-1\right)-9\left(x-1\right)\)
=\(\left(x-1\right)\left(4x^2-9\right)\)
=\(\left(x-1\right)\left(2x-3\right)\left(2x+3\right)\)
\(xy-x^2+x-y\)
=\(x\left(y-x\right)+\left(x-y\right)\)
=\(x\left(y-x\right)-\left(y-x\right)\)
=\(\left(y-x\right)\left(x-1\right)\)
Nhớ cho mình 1 đúng nha
1)\(\left(a^2-1\right)^2-4a^2\)
\(=\left(a^2+1-2a\right)\left(a^2+1+2a\right)\)
\(=\left(a-1\right)^2\left(a+1\right)^2\)
2)\(\left(4x^2-3x-18\right)^2-\left(4x^2+3x\right)^2\)
\(=\left(4x^2-3x-18-4x^2-3x\right)\left(4x^2-3x-18+4x^2+3x\right)\)
\(=\left(-6x-18\right)\left(8x^2-18\right)\)
\(=-3\left(2x+6\right).2\left(4x^2-9\right)\)
\(=-6\left(2x+6\right)\left(2x-3\right)\left(2x+3\right)\)
K NHA!!!
a) 2x3 + 8x2 - 8x
= 2x(x2 + 4x - 4)
= 2x(x2 + 4x + 4 - 8)
= 2x[(x + 2)2 - 8]
= \(2x\left(x+2-\sqrt{8}\right)\left(x+2+\sqrt{8}\right)\)
b) a2 - b2 + 4a + 4b
= (a - b)(a + b) + 4(a + b)
= (a + b)(a - b + 4)
c) x2 - 2x - 3
= x2 + x - 3x - 3
= x(x + 1) - 3(x + 1)
= (x + 1)(x - 3)
d) x2 - 4x - 3
= x2 - 4x + 4 - 7
= (x + 2)2 - 7
= \(\left(x+2-\sqrt{7}\right)\left(x+2+\sqrt{7}\right)\)
a) \(4x^2-12x+9=\left(2x\right)^2-2\cdot2x\cdot3+3^2=\left(2x-3\right)^2\)
b) \(4x^2+4x+1=\left(2x\right)^2+2\cdot2x\cdot1+1^2=\left(2x+1\right)^2\)
c) \(1+12x+36x^2=1^2+2\cdot1\cdot6x+\left(6x\right)^2=\left(1+6x\right)^2\)
d) \(9x^2-24xy+16y^2=\left(3x\right)^2-2\cdot3x\cdot4y+\left(4y\right)^2=\left(3x-4y\right)^2\)
e) \(8x^3+1=\left(2x\right)^3+1^3=\left(2x+1\right)\left(4x^2+2x+1\right)\)
f) \(-8x^3+27=3^3-\left(2x\right)^3=\left(3-2x\right)\left(9+6x+4x^2\right)\)
\(81x^2-6yz-9y^2-z^2=81x^2-\left(6yz+9y^2+z^2\right)\)
\(=81x^2-\left(9y^2+6xy+z^2\right)=81x^2-\left(3y+z\right)^2\)
\(=\left(9x-3y-z\right)\left(9x+3y+z\right)\)
4a2=4b2-4a+1
=(2a)2-2*2a*1+12-4b2= (2a-1)2-(2b)2(2a-1-2b)(2a-1+2b)
a, \(2x^2+2x+5x+5=2x\left(x+1\right)+5\left(x+1\right)=\left(2x+5\right)\left(x+1\right)\)
b,\(2x^2-2x+5x-5=2x\left(x-1\right)+5\left(x-1\right)=\left(2x+5\right)\left(x-1\right)\)
c,\(x^3-3x^2+1-3x=\left(x^3+1\right)-3x\left(x+1\right)=\left(x+1\right)\left(x^2-x+1\right)-3x\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-4x+1\right)\)
d,\(x^2-4x-5=x^2+x-5x-5=x\left(x+1\right)-5\left(x+1\right)=\left(x-5\right)\left(x+1\right)\)
e,\(\left(a^2+1\right)^2-4a^2=\left(a^2+1\right)^2-\left(2a\right)^2=\left(a^2-2a+1\right)\left(a^2+2a+1\right)=\left(a-1\right)^2\left(a+1\right)^2\)
\(1,\\ a,\left(5x-6y\right)\left(2x^2-3xy-4y^2\right)\\ =10x^3-15x^2y-20xy^2-12x^2y+18xy^2+24y^3\\ =10x^3-27x^2y-2xy^2+24y^3\\ b,Làmtươngtự\\ 2,\\ a,4a^2-4a+1-b^2\\ =\left(4a^2-4a+1\right)-b^2\\ =\left(2a-1\right)^2-b^2\\ =\left(2a-1-b\right)\left(2a-1+b\right)\\ b,4x^3-4x^2-9x+9\\ =4x^2\left(x-1\right)-9\left(x-1\right)\\ =\left(x-1\right)\left(4x^2-9\right)\\ =\left(x-1\right)\left(2x-3\right)\left(2x+3\right)\)
a) \(4a^2-4a+1-b^2=\left(2a\right)^2-2.2.a+1-b^2\\ =\left(2a-1\right)-b^2=\left(2a-1+b\right)\left(2a-1-b\right)\)
b) \(4x^3-4x^2-9x+9=4x^2\left(x-1\right)-9\left(x-1\right)\\ =\left(x-1\right)\left(4x^2-3^2\right)=\left(x-1\right)\left(2x-3\right)\left(2x+3\right)\)
a) \(4a^2-4a+1-b^2\)
\(=\left(2a-1\right)^2-b^2\)
\(=\left(2a-b-1\right)\left(2a+b-1\right)\)
b) \(4x^3-4x^2-9x+9\)
\(=4x^2\left(x-1\right)-9\left(x-1\right)\)
\(=\left(4x^2-9\right)\left(x-1\right)\)
\(=\left(2x-3\right)\left(2x+3\right)\left(x-1\right)\)