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a) \([(x-y)3 + (y-z)3]+ (z-x)3\)=\(\left(x-y+y-z\right)\left[\left(x-y\right)^2-\left(x-y\right)\left(y-z\right)+\left(y-z\right)^2\right]-\left(x-z\right)^3\)
\(=\left(x-z\right)\left[\left(\left(x-y\right)^2-\left(x-y\right)\left(y-z\right)+\left(y-z\right)^2-\left(x-z\right)^2\right)\right]\)
\(=\left(x-z\right)\left[\left(x-y\right)\left(x-y-y+z\right)+\left(y-z-x+z\right)\left(y-z+x-z\right)\right]=\left(x-z\right)\left[\left(x-2y+z\right)\left(x+z\right)-\left(x-y\right)\left(x+y-2z\right)\right]\)
\(=\left(x-z\right)\left(x-y\right)\left(x-2y+z-x-y+2z\right)=\left(x-z\right)\left(x-y\right)\left(z-y\right)3\)
b) \(=y^2\left(x^2y-x^3+z^3-z^2y\right)-z^2x^2\left(z-x\right)=y^2\left[-y\left(z^2-x^2\right)-\left(z^3-x^3\right)\right]-z^2x^2\left(z-x\right)\)
\(=y^2\left(z-x\right)\left(-yz-xy-z^2-zx-x^2\right)-z^2x^2\left(z-x\right)=\left(z-x\right)\left(-y^3z-xy^2-z^2y^2-xyz-x^2y^2-z^2x^2\right)\)
đến đây coi như là thành nhân tử rồi nha. em muốn gọn thì ráng ngồi nghĩ rồi tách nha. chỉ cần nhóm mấy cái có ngoặc giống nhau là đc. k khó đâu. chịu khó nghĩ để rèn luyện nha
c) \(x^8+2x^4+1-x^4=\left(x^4+1\right)^2-x^4=\left(x^4+1-x^2\right)\left(x^4+1+x^2\right)\)
\(\left(9a^3-6a^2\right)+\left(6a^2-4a\right)+\left(-9a+6\right)=3a^2\left(3a-2\right)+2a\left(3a-2\right)-3\left(3a-2\right)=\left(3a-2\right)\left(3a^2+2a-3\right)\)
d) em sửa đề đi. đề sai rồi. đồng nhất hệ số phải có dấu bằng nha.
có gì liên hệ chị. đúng nha ;)
\(1.=5xy\left(x-2y\right)\)
\(2.=\left(5-y\right)\left(x-y\right)\)
\(3.=y\left(x-z\right)-7\left(x-z\right)=\left(y-7\right)\left(x-z\right)\)
\(5.=2x\left(3y-7z\right)-6y\left(3y-7z\right)=\left(2x-6y\right)\left(3y-7x\right)\)
\(4.=27x^2\left(y-1\right)+9x^3\left(y-1\right)=9x^2\left(3+x\right)\left(y-1\right)\)
a) x2 + 6x + 9 = x2 + 2 . x . 3 + 32 = (x + 3)2
b) 10x – 25 – x2 = -(-10x + 25 +x2) = -(25 – 10x + x2)
= -(52 – 2 . 5 . x – x2) = -(5 – x)2
c) 8x3 - 1/8 = (2x)3 – (1/2)3 = (2x - 1/2)[(2x)2 + 2x . 12 + (1/2)2]
= (2x - 1/2)(4x2 + x + 1/4)
d)1/25x2 – 64y2 = (1/5x)2(1/5x)2- (8y)2 = (1/5x + 8y)(1/5x - 8y)
a) 3x(x + 7)2 - 11x2(x + 7) + 9(x + 7) = (x + 7)[3x(x + 7) - 11x2 + 9) = (x + 7)(3x2 + 21x - 11x2 + 9)
= (x + 7)(-8x2 + 21x + 9)(-8x2 + 24x - 3x + 9) = (x + 7)[-8x(x - 3) - 3(x - 3)] = -(x + 7)(8x + 3)(x - 3)
b) 3x(x - 9)2 - (9 - x)3 = 3x(x - 9)2 + (x - 9)3 = (x - 9)2(3x + x - 9) = (x - 9)2(4x - 9)
c) pm + 2.q - pm + 1.q3 - p2.qn + 1 + p.qn + 3 = (pm + 2.q - p2.qn + 1) - (pm + 1.q3 - p.qn + 3)
= p2.q(pm - qn) - p.q3(pm - qn) = pq(pm - qn)(p - q2)
d) x2y2z + xy2z2 + x2yz = xyz(xy + yz + x)
a) \(3x\left(x+7\right)^2-11x^2\left(x+7\right)+9\left(x+7\right)\)
\(=\left(x+7\right)\left[3x\left(x+7\right)-11x^2+9\right]=\left(x+7\right)\left(3x^2+21x-11x^2+9\right)\)
\(=\left(x+7\right)\left(-8x^2+21x+9\right)=\left(x+7\right)\left[\left(-8x^2+24x\right)-\left(3x-9\right)\right]\)
\(=\left(x+7\right)\left[-8x\left(x-3\right)-3\left(x-3\right)\right]=-\left(x+7\right)\left(x-3\right)\left(8x+3\right)\)
b) \(3x\left(x-9\right)^2-\left(9-x\right)^3=3x\left(x-9\right)^2+\left(x-9\right)^3\)
\(=\left(x-9\right)^2\left(3x+x-9\right)=\left(x-9\right)^2\left(4x-9\right)\)
c) \(p^{m+2}.q-p^{m+1}.q^3-p^2.q^{n+1}+p.q^{n+3}\)
\(=p^{m+1}.q\left(p-q^2\right)-p.q^{n+1}\left(p-q^2\right)\)\(=p.q.\left(p-q^2\right).\left(p^m.q^n\right)\)
d) \(x^2y^2z+xy^2z^2+x^2yz=xyz\left(xy+yz+x\right)\)