Câu hỏi của Diệu Hà Thịnh

Question

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Nguyễn Lê Phước Thịnh · Accepted Answer

j: $81x^4+4y^4$$=81x^4+36x^2y^2+4y^4-36x^2y^2$$=\left(9x^2+2y^2\right)^2-\left(6xy\right)^2$$=\left(9x^2+2y^2+6xy\right)\left(9x^2+2y^2-6xy\right)$g: $\left(x^3+x+1\right)\left(x^3+x\right)-2$$=\left(x^3+x\right)^2+\left(x^3+x\right)-2$$=\left(x^3+x+2\right)\left(x^3+x-1\right)$$=\left(x^3+x-1\right)\left(x^3-x+2x+2\right)$$=\left(x^3+x-1\right)\left[x\left(x-1\right)\left(x+1\right)+2\left(x+1\right)\right]$$=\left(x+1\right)\left(x^3+x-1\right)\left(x^2-x+2\right)$h: $\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)+1$$=\left(x^2+5x+4\right)\left(x^2+5x+6\right)+1$$=\left(x^2+5x\right)^2+10\left(x^2+5x\right)+24+1$$=\left(x^2+5x\right)^2+10\left(x^2+5x\right)+25=\left(x^2+5x+5\right)^2$j: $-\left(x^2+2\right)^2+4x\left(x^2+2\right)-3x^2$$=-\left[\left(x^2+2\right)^2-4x\left(x^2+2\right)+3x^2\right]$$=-\left(x^2+2-3x\right)\left(x^2+2-x\right)=-\left(x^2-x+2\right)\left(x-1\right)\left(x-2\right)$Câu trả lời: j: $81x^4+4y^4$$=81x^4+36x^2y^2+4y^4-36x^2y^2$$=\left(9x^2+2y^2\right)^2-\left(6xy\right)^2$$=\left(9x^2+2y^2+6xy\right)\left(9x^2+2y^2-6xy\right)$g: $\left(x^3+x+1\right)\left(x^3+x\right)-2$$=\left(x^3+x\right)^2+\left(x^3+x\right)-2$$=\left(x^3+x+2\right)\left(x^3+x-1\right)$$=\left(x^3+x-1\right)\left(x^3-x+2x+2\right)$$=\left(x^3+x-1\right)\left[x\left(x-1\right)\left(x+1\right)+2\left(x+1\right)\right]$$=\left(x+1\right)\left(x^3+x-1\right)\left(x^2-x+2\right)$h: $\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)+1$$=\left(x^2+5x+4\right)\left(x^2+5x+6\right)+1$$=\left(x^2+5x\right)^2+10\left(x^2+5x\right)+24+1$$=\left(x^2+5x\right)^2+10\left(x^2+5x\right)+25=\left(x^2+5x+5\right)^2$j: $-\left(x^2+2\right)^2+4x\left(x^2+2\right)-3x^2$$=-\left[\left(x^2+2\right)^2-4x\left(x^2+2\right)+3x^2\right]$$=-\left(x^2+2-3x\right)\left(x^2+2-x\right)=-\left(x^2-x+2\right)\left(x-1\right)\left(x-2\right)$

HT.Phong (9A5) · Answer

g) $\left(x^3+x+1\right)\left(x^3+x\right)-2$$=\left[\left(x^3+x\right)+1\right]\left(x^3+x\right)-2$$=\left(x^3+x\right)^2+\left(x^3+x\right)-2$$=\left(x^3+x\right)^2-\left(x^3+x\right)+2\left(x^3+x\right)-2$$=\left(x^3+x\right)\left(x^3+x-1\right)+2\left(x^3+x-1\right)$$=\left(x^3+x-1\right)\left(x^3+x+2\right)$$=\left(x+1\right)\left(x^2-x+2\right)\left(x^3+x-1\right)$h) $\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)+1$$=\left[\left(x+1\right)\left(x+4\right)\right]\left[\left(x+2\right)\left(x+3\right)\right]+1$$=\left(x^2+5x+4\right)\left(x^2+5x+6\right)+1$$=\left[\left(x^2+5x+5\right)-1\right]\left[\left(x^2+5x+5\right)+1\right]+1$$=\left(x^2+5x+5\right)^2-1+1$$=\left(x^2+5x+5\right)^2$i) $-\left(x^2+2\right)^2+4x\left(x^2+2\right)-3x^2$  $=-\left(x^2+2\right)^2+3x\left(x^2+2\right)+x\left(x^2+2\right)-3x^2$$=-\left(x^2+2\right)\left(x^2-3x+2\right)+x\left(x^2-3x+2\right)$$=\left(x^2-3x+2\right)\left(-x^2+x-2\right)$$=\left(x-1\right)\left(x-2\right)\left(-x^2+x-2\right)$j) $81x^4+4y^4$ $=\left(9x^2\right)^2+\left(2y^2\right)^2$$=\left(9x^2\right)^2+2\cdot9x^2\cdot2y^2+\left(2y^2\right)^2-2\cdot9x^2\cdot2y^2$$=\left(9x^2+2y^2\right)-36x^2y^2$$=\left(9x^2-6xy+2y^2\right)\left(9x^2+6xy+2y^2\right)$Câu trả lời: g) $\left(x^3+x+1\right)\left(x^3+x\right)-2$$=\left[\left(x^3+x\right)+1\right]\left(x^3+x\right)-2$$=\left(x^3+x\right)^2+\left(x^3+x\right)-2$$=\left(x^3+x\right)^2-\left(x^3+x\right)+2\left(x^3+x\right)-2$$=\left(x^3+x\right)\left(x^3+x-1\right)+2\left(x^3+x-1\right)$$=\left(x^3+x-1\right)\left(x^3+x+2\right)$$=\left(x+1\right)\left(x^2-x+2\right)\left(x^3+x-1\right)$h) $\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)+1$$=\left[\left(x+1\right)\left(x+4\right)\right]\left[\left(x+2\right)\left(x+3\right)\right]+1$$=\left(x^2+5x+4\right)\left(x^2+5x+6\right)+1$$=\left[\left(x^2+5x+5\right)-1\right]\left[\left(x^2+5x+5\right)+1\right]+1$$=\left(x^2+5x+5\right)^2-1+1$$=\left(x^2+5x+5\right)^2$i) $-\left(x^2+2\right)^2+4x\left(x^2+2\right)-3x^2$  $=-\left(x^2+2\right)^2+3x\left(x^2+2\right)+x\left(x^2+2\right)-3x^2$$=-\left(x^2+2\right)\left(x^2-3x+2\right)+x\left(x^2-3x+2\right)$$=\left(x^2-3x+2\right)\left(-x^2+x-2\right)$$=\left(x-1\right)\left(x-2\right)\left(-x^2+x-2\right)$j) $81x^4+4y^4$ $=\left(9x^2\right)^2+\left(2y^2\right)^2$$=\left(9x^2\right)^2+2\cdot9x^2\cdot2y^2+\left(2y^2\right)^2-2\cdot9x^2\cdot2y^2$$=\left(9x^2+2y^2\right)-36x^2y^2$$=\left(9x^2-6xy+2y^2\right)\left(9x^2+6xy+2y^2\right)$

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