ptdttnt:2x^2-4x
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NL
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AA
1
MT
5 tháng 8 2015
1. (x^2-25)^2-(x-5)^2
=(x-5)2(x+5)2-(x-5)2
=(x-5)2.[(x+5)2-1)
=(x-5)2.(x+5-1)(x+5+1)
=(x-5)2.(x+4)(x+6)
2. (4x^2-25)^2-9(2x-5)^2
=(2x-5)2(2x+5)2-9.(2x-5)2
=(2x-5)2[(2x+5)2-9]
=(2x-5)2(2x+5-3)(2x+5+3)
=(2x-5)2(2x+2)(2x+8)
=4(2x-5)2(x+1)(x+4)
KL
1
27 tháng 5 2022
a: \(\left(2x+1\right)\left(2x+3\right)\left(x+1\right)^2-18\)
\(=\left[\left(2x+2\right)^2-1\right]\left(x+1\right)^2-18\)
\(=4\left(x+1\right)^4-\left(x+1\right)^2-18\)
\(=4\left(x+1\right)^4-9\left(x+1\right)^2+8\left(x+1\right)^2-18\)
\(=\left(x+1\right)^2\left[4\left(x+1\right)^2-9\right]+2\left[4\left(x+1\right)^2-9\right]\)
\(=\left[\left(2x+2\right)^2-9\right]\left[\left(x+1\right)^2+2\right]\)
\(=\left(2x+5\right)\left(2x-1\right)\left(x^2+2x+3\right)\)
b: \(\left(x^2+4x+3\right)\left(x^2+12x+35\right)+15\)
\(=\left(x+1\right)\left(x+3\right)\left(x+5\right)\left(x+7\right)+15\)
\(=\left(x^2+8x+7\right)\left(x^2+8x+15\right)+15\)
\(=\left(x^2+8x\right)^2+22\left(x^2+8x\right)+105+15\)
\(=\left(x^2+8x\right)^2+22\left(x^2+8x\right)+120\)
\(=\left(x^2+8x+10\right)\left(x^2+8x+12\right)\)
\(=\left(x^2+8x+10\right)\left(x+2\right)\left(x+6\right)\)
c: \(\left(x-3\right)\left(x-5\right)\left(x-6\right)\left(x-10\right)-24x^2\)
\(=\left(x^2-13x+30\right)\left(x^2-11x+30\right)-24x^2\)
\(=\left(x^2+30\right)^2-24x\left(x^2+30\right)+143x^2-24x^2\)
\(=\left(x^2+30\right)^2-24x\left(x^2+30\right)+119x^2\)
\(=\left(x^2-17x+30\right)\left(x^2-7x+30\right)\)
\(=\left(x-2\right)\left(x-15\right)\left(x^2-7x+30\right)\)
29 tháng 10 2016
\(4x^3-5x^2+6x+9\)
\(=\left(4x^3+3x^2\right)-\left(8x^2+6x\right)+\left(12x+9\right)\)
\(=x^2\left(4x+3\right)-2x\left(4x+3\right)+3\left(4x+3\right)\)
\(=\left(4x+3\right)\left(x^2-2x+3\right)\)
14 tháng 10 2018
x2+4x+3
=x2+x+3x+3
=x(x+1)+3(x+1)
=(x+1)(x+3)
k cho mk nhé
NT
0