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a) -5xy(3x2y – 5xy +y2)
=-15x3y2+25x2y2-5xy3
b) (x + 8)2 -2(x + 8) (x – 2) + (x – 2)2
=[(x+8)-(x-2)]2
=(x+8-x+2)2
=102
=100
\(a,-5xy\left(3x^2y-5xy+y^2\right)=-15x^3y^2+25x^2y^2-5xy^3\)
\(b,\left(x+8\right)^2-2\left(x+8\right)\left(x-2\right)+\left(x-2\right)^2=\left[x+8-\left(x-2\right)\right]^2=\left[x+8-x+2\right]^2=10^2=100\)
Bài1: Phân tích các đa thức sau thành nhân tử
a)36-4x2+4xy-y2
\(=6^2-\left(4x^2-4xy+y^2\right)\)
\(=6^2-\left(2x-y\right)^2\)
\(=\left(6+2x-y\right)\left(6-2x+y\right)\)
b)2x4+3x2-5
\(=2x^4-2x^2+5x^2-5\)
\(=2x^2\left(x^2-1\right)+5\left(x^2-1\right)\)
\(=\left(2x^2+5\right)\left(x^2-1\right)\)
\(=\left(2x^2+5\right)\left(x-1\right)\left(x+1\right)\)
B1:a)\(36-4x^2+4xy-y^2=36-\left(4x^2-4xy+y^2\right)=6^2-\left(2x-y\right)^2\)
\(=\left(6-2x+y\right)\left(6+2x-y\right)\)
c)\(a^3-ab^2+a^2+b^2-2ab=a\left(a^2-b^2\right)+\left(a-b\right)^2\)\(=a\left(a-b\right)\left(a+b\right)+\left(a-b\right)^2=\left(a-b\right)\left(a^2+ab+a-b\right)\)
d)\(x^2-\left(a^2+b^2\right)x+a^2b^2=x^2-a^2x-b^2x+a^2b^2\)\(=x\left(x-a^2\right)-b^2\left(x-a^2\right)=\left(x-a^2\right)\left(x-b^2\right)\)
e)\(x\left(x-y\right)+x^2-y^2=x\left(x-y\right)+\left(x-y\right)\left(x+y\right)\)\(=\left(x-y\right)\left(x+x+y\right)=\left(x-y\right)\left(2x+y\right)\)
a) \(x^3\left(3x^2-x-\dfrac{1}{2}\right)=3x^5-x^4-\dfrac{1}{2}x^3\)
b) \(\left(5xy-x^2+y\right)\dfrac{2}{5}xy^2=2x^2y^3-\dfrac{2}{5}x^3y^2+\dfrac{2}{5}xy^3\)
c) \(\left(4x^3-3xy^2+2xy\right)\left(-\dfrac{1}{3}x^2y\right)=\dfrac{-4}{3}x^5y+x^3y^3-\dfrac{2}{3}x^3y^2\)