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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) \(x^2y^2z+xy^2z^2+x^2yz=xyz\left(xy+yz+x\right)\)
những bài này dễ lắm bn à, chỉ đơn thuần là áp dụng hđt thui
a) (x+1)(4x-8) =0
x+1=0
x= -1
4x-8 =0
x = 2
b) = 2(x+1)(x+1) = 2(x+1)2
..........................
a) \(x^3-x^2-x+1\)
\(=\left(x^3-x^2\right)-\left(x-1\right)\)
\(=x^2\left(x-1\right)-\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2-1\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x-1\right)\)
b) \(x^3-3x+1-3x^2\)
\(=\left(x^3+1\right)-\left(3x^2+3x\right)\)
\(=\left(x+1\right)\left(x^2-x+1\right)-3x\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-x+1-3x\right)\)
\(=\left(x+1\right)\left(x^2-4x+1\right)\)
c) \(x^2-4x-5\)
\(=x^2.2x.2+4-9\)
\(=\left(x-2\right)^2-3^2\)
\(=\left(x-2+3\right)\left(x-2-3\right)\)
\(=\left(x+1\right)\left(x-5\right)\)
c) x2 - 4x - 5
= x2-5x+x-5
=(x2-5x)+(x-5)
=x(x-5)+(x-5)
=(x-5)(x+1)
mk lm tp nè
b)(x+1)\(^2\)+(x+3)(x-3)=(x+1)\(^2\)-(x+3)(x+3)
=(x+1)\(^2\)-(x+3)\(^2\)
=(x+1+x+3)(x+1-x+3)
=(2x+4)4
Đặt \(x^2+1=t\)
Ta có: \(\left(x^2+1\right)^2+3x\left(x^2+1\right)+2x^2\)
\(=t^2+3xt+2t^2\)
\(=t^2+xt+2xt+2t^2\)
\(=t\left(t+x\right)+2x\left(t+x\right)\)
\(=\left(t+x\right)\left(t+2x\right)\)
\(=\left(x^2+1+x\right)\left(x^2+1+2x\right)\)
\(=\left(x^2+x+1\right)\left(x+1\right)^2\)
Chúc bạn học tốt
a) x.(1-x)+(x-1)2
=x.1-x2+x2-2.x2.1+12
=x-x2+x2-2.x2+1
=(-x2+x2-2x2)+1
=-2x2+1
b)(x+1)2-3.(x+1)
=x2+2.x2.1+12-3.x+3
=x2+2.x2+1-3x+3
=(x2+2x2)+(1+3)-3x
=3x2-3x+4
c)3x.(x-1)2-(1-x)3
=3x.x2-2,x2.1+12-13-3.12.x+3.x.12=3x.x2-2x2+1-1-3x+3x=(3x-3x+3x)(x2-2x2)(1-1)=3x.(-x2)