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a, 4x4+1
=(2x)2+1
=(2x+1)(2x-1)
b,c tách làm bình phương rồi làm tương tự
a )\(x^2-2x-4y^2-4y=\left(x^2-2x+1\right)-\left(4y^2+4y+1\right)\)
\(=\left(x-1\right)^2-\left(2y+1\right)^2=\left(x-2y-2\right)\left(x+2y\right)\)
b )\(x^4+2x^3-4x-4=\left(x^4+2x^3+x^2\right)-\left(x^2+4x+4\right)\)
\(=\left(x^2+x\right)^2-\left(x+2\right)^2=\left(x^2+2x+2\right)\left(x^2-2\right)\)
c ) \(x^2\left(1-x^2\right)-4-4x^2=x^2-x^4-4-4x^2\)
\(=x^2-\left(x^2+2\right)^2=\left(x-x^2-2\right)\left(x^2+x+2\right)\)
a) \(x^4+4\)
\(=\left(x^2\right)^2+2\cdot x^2\cdot2+2^2-2\cdot x^2\cdot2\)
\(=\left(x^2+2\right)^2-\left(2x\right)^2\)
\(=\left(x^2-2x+2\right)\left(x^2+2x+2\right)\)
b) \(4x^8+1\)
\(=\left(2x^4\right)^2+2\cdot2x^4\cdot1+1^2-2\cdot2x^4\cdot1\)
\(=\left(2x^4+1\right)-\left(2x^2\right)^2\)
\(=\left(2x^4-2x^2+1\right)\left(2x^4+2x^2+1\right)\)
a/ \(x^4+4=\left(x^2\right)^2+4x^2+4-4x^2=\left(x^2+2\right)^2-4x^2=\left(x^2-4x+2\right)\left(x^2+4x+2\right)\)
b/ \(4x^8+1=\left(2x^4\right)^2+1=\left(2x^4\right)^2+4x^4+1-4x^4=\left(2x^4+1\right)^2-4x^2=\left(2x^4-2x+1\right)\left(2x^4+2x+1\right)\)
Bài làm ai trên 11 điểm tích mình thì mình tích lại
Ông tùng hơn tùng số tuổi là :
29 + 32 = 61 (tuổi )
Vậy ông của tùng hơn tùng 61 tuổi
\(\left(x^2+x\right)^2+4x^2+4x-12\)
\(=x^4+2x^3+5x^2+4x-12\)
\(=x^4-x^3+3x^3-3x^2+8x^2-8x+12x-12\)
\(=x^3.\left(x-1\right)+3x^2.\left(x-1\right)+8x.\left(x-1\right)+12.\left(x-1\right)\)
\(=\left(x-1\right).\left(x^3+3x^2+8x+12\right)=\left(x-1\right).\left(x+2\right).\left(x^2+x+6\right)\)
p/s: sai sót bỏ qua
a) \(x^4+4=x^4+4x^2+4-4x^2=\left(x^2+2\right)^2-4x^2=\left(x^2-2x+2\right)\left(x^2+2x+2\right)\)
b) \(4x^8+1=4x^8+4x^4+1-4x^4=\left(2x^4+1\right)^2-4x^4=\left(2x^4-2x^2+1\right)\left(2x^4+2x^2+1\right)\)
d) \(x^2+14x+48=\left(x+7\right)^2-1=\left(x+7+1\right)\left(x+7-1\right)=\left(x+8\right)\left(x+6\right)\)
\(x^3+4x^2+4x+3\)
\(=x^3+3x^2+x^2+3x+x+3\)
\(=x^2\left(x+3\right)+x\left(x+3\right)+\left(x+3\right)\)
\(=\left(x+3\right)\left(x^2+x+1\right)\)
\(x^2-y^2+4y-4\)
\(=x^2-\left(y^2-4y+4\right)\)
\(=x^2-\left(y-2\right)^2\)
\(=\left(x-y+2\right)\left(x+y-2\right)\)
\(x^4+x^3y-xy^3-y^4\)
\(=x^3\left(x+y\right)-y^3\left(x+y\right)\)
\(=\left(x+y\right)\left(x^3-y^3\right)\)
\(=\left(x+y\right)\left(x-y\right)\left(x^2+xy+y^2\right)\)
Chúc bạn học tốt.
a) x^4+4=x^4+4x^2+4-4x^2
=(x^2+2)^2-4x^2
=(x^2+2)^2-(2x)^2
=(x^2-2x+2)(x ^2+2x+2).
a, \(x^4+4=x^4+4+4x^2-4x^2\)
\(=\left(x^4+4x^2+4\right)-4x^2\)
\(=\left(x^2+2\right)^2-\left(2x\right)^2\)
\(=\left(x^2+2-2x\right)\left(x^2+2+2x\right)\)
b, \(4x^4+1=4x^4+1+4x^2-4x^2\)
\(=\left(4x^4+4x^2+1\right)-4x^2\)
\(=\left(2x^2+1\right)^2-\left(2x\right)^2\)
\(=\left(2x^2+1-2x\right)\left(2x^2+1+2x\right)\)