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1: \(=x^2+6x+9-y^2\)
\(=\left(x+3\right)^2-y^2\)
\(=\left(x+3+y\right)\left(x+3-y\right)\)
2: \(x^2-2xy+y^2-25\)
\(=\left(x-y\right)^2-25\)
\(=\left(x-5-y\right)\left(x+5-y\right)\)
4: \(=y\left(x-y\right)-5\left(x-y\right)=\left(x-y\right)\left(y-5\right)\)
5: \(=x^3\left(x+3\right)-9\left(x+3\right)\)
\(=\left(x+3\right)\left(x^3-9\right)\)
a) (x3 + 8y3) : (2y + x)
= (x + 2y)(x2 - 2xy + 4y2) : (2y + x)
= x2 - 2xy + 4y2
b) (x3 + 3x2y + 3xy2 + y3) : (2x + 2y)
= (x + y)3 : 2(x + y)
= \(\dfrac{\left(x+y\right)^2}{2}\)
c) (6x5y2 - 9x4y3 + 15x3y4) : 3x3y2
= 3x3y2(2x2 - 3xy + 5y2) : 3x3y2
= 2x2 - 3xy + 5y2
\(a,\left(2x-y\right)\left(4x^2-2xy+y^2\right)=\left(2x-y\right)\left(2x-y\right)^2=\left(2x-y\right)^3\)
\(b,\left(6x^5y^2-9x^4y^3+15x^3y^4\right):3x^3y^2=2x^2-3xy+5y^2\)
\(c,\left(2x^3-21x^2+67x-60\right):\left(x-5\right)=\left(2x^3-10x^2-11x^2+55x+12x-60\right):x-5=\left[2x^2\left(x-5\right)-11x\left(x-5\right)+12\left(x-5\right)\right]:\left(x-5\right)=\left(x-5\right)\left(2x^2-11x+12\right)\left(x-5\right):\left(x-5\right)=2x^2-11x+12\)
1. Câu hỏi của Koy Pham - Toán lớp 8 | Học trực tuyến
2.
a. \(\left(x-3\right)\left(x^2+3x+9\right)-\left(54+x^3\right)\)
\(=\left(x^3-27\right)-\left(54+x^3\right)\)
\(=x^3-27-54-x^3\)
\(=-81\)
b. \(\left(3x+y\right)\left(9x^2-3xy+y^2\right)-\left(3x-y\right)\left(9x^2+xy+y^2\right)\)
\(=\left[\left(3x\right)^3+y^3\right]-\left[\left(3x\right)^3-y^3\right]\)
\(=2y^3\)
\(A=27x^3y^3-18x^2y^2-1-9x^2y^2+9xy\)
\(=27x^3y^3-27x^2y^2+9xy-1\)
=(3xy-1)^3
=(21-1)^3=20^3=8000
\(A=\left(3x-1\right)\left(9x^2+3x+1\right)\)
\(=\left(3x\right)^3-1^3\)
\(=27x^3-1\)
\(B=\left(5x+3\right)\left(25x^2-15x+9\right)\)
\(=\left(5x\right)^3+3^3\)
\(=125x^3+27\)
\(\left(3x^4y^3-9x^2y^2+25xy^3\right):xy^2-3x^3y+9x+25\)
\(=3x^4y^3:xy^3-9x^2y^2:xy^2+25xy^3:xy^2-3x^3y-9x+25\)
\(=3x^3-9x+25y-3x^3y-9x+25\)
\(=3x^3-18x+25y-3x^3y+25\)