Question

phân tích các đa thức sao thành nhân tử

a.x²-10x+25

b.(2x-3)²-x²

c.x³+2x²y+xy²-9x

Answer 1

a) x² - 10x + 25

= x² - 2.x.5 + 5²

= (x - 5)²

b) (2x - 3)² - x²

= (2x - 3 - x)(2x - 3 + x)

= (x - 3)(3x - 3)

= 3(x - 3)(x - 1)

c) x³ + 2x²y+ xy² - 9x

= x(x² + 2xy + y² - 9)

= x[(x + y)² - 3²]

= x(x + y - 3)(x + y + 3)

Answer 2

a/\(x^2-10x+25\)
\(=\left(x-5\right)^2\)
b/\(\left(2x-3\right)^2-x^2\)
\(=\left(2x-3-x\right)\left(2x-3+x\right)\)
\(=\left(x-3\right)\left(3x-3\right)\)
\(=3\left(x-3\right)\left(x-1\right)\)
c/\(x^3+2x^2+xy^2-9x\)
\(=x\left(x^2+2x+y^2-9\right)\)
\(=x\left[\left(x+y\right)^2-3^2\right]\)
\(=x\left(x+y-3\right)\left(x+y+3\right)\)
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