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\(\left(\frac{x^4}{2}\right)-2x^2\)
\(=\left(\frac{x^2}{\sqrt{2}}\right)^2-2x^2\)
\(=\left(\frac{x^2}{\sqrt{2}}+2x\right)\left(\frac{x^2}{\sqrt{2}}-2x\right)\)
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(x2+2x)2-2(x2+2x)-3
=(x2+2x)(x2+2x-2)-3
Đặt t=x2+2x ta có:
t(t-2)-3=t2-2t-3
=(t-3)(t+1)=(x2+2x-3)(x2+2x+1)
=(x-1)(x+3)(x+1)2
(x^2+2x)^2-2(x^2+2x)-3
=(x^2+2x)(x^2+2x-2)-3
=(x^2+2x)(x^2+2x-5)
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=x2 (1-x2 ) + 2x2 (x+1)
=-x2 (x2-1) + 2x2 (x+1)
= -x2 (x+1)(x-1) + 2x2 (x-1)
Đến đây đã xuất hiện nhân tử chung là (x-1)
Em chỉ việc nhóm vào là xong
Chúc em học giỏi!
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a) \(45+x^3-5x^2-9x\)
\(\Leftrightarrow\left(45-9x\right)+\left(x^3-5x^2\right)\)
\(\Leftrightarrow-9\left(x-5\right)+x^2\left(x-5\right)\)
\(\Leftrightarrow\left(x-5\right)\left(x-3\right)\left(x+3\right)\)
TK NKA !!!
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\(x^8+3x^4+4\)
\(=\left(x^8-x^6+2x^4\right)+\left(x^6-x^4+2x^2\right)+\left(2x^4-2x^2+4\right)\)
\(=x^4\left(x^4-x^2+2\right)+x^2\left(x^4-x^2+2\right)+2\left(x^4-x^2+2\right)\)
\(=\left(x^4+x^2+2\right)\left(x^4-x^2+2\right)\)
\(4x^4+4x^3+5x^2+2x+1\)
\(=\left(4x^4+2x^3+2x^2\right)+\left(2x^3+x^2+x\right)+\left(2x^2+x+1\right)\)
\(=2x^2\left(2x^2+x+1\right)+x\left(2x^2+x+1\right)+\left(2x^2+x+1\right)\)
\(=\left(2x^2+x+1\right)^2\)
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khó quá mk nản chí rùi huhu!!
3463465655775676876897756232544545465657578768
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\(x^4-2x^2=\left(x^4-2x^2+1\right)-1\)
\(=\left(x^2-1\right)^2-1^2\)
\(=\left(x^2-1-1\right)\left(x^2-1+1\right)\)
\(=x^2.\left(x^2-2\right)\)