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Ta có :
a3m+2a2m+am
= am(a2m+2am+1)
= am[(am)2+2am+1]
= am(am+1)2
\(a\left(a+2b\right)^3-b\left(2a+b\right)^3\)
\(=a\left(a ^3+3.a^22b+3.a2b^2+2b^3\right)-b\left(2a^3+3.2a^2.b+3.2a.b^2+b^3\right)\)
\(=a\left(a^3+6a^2b+6ab^2+8b^3\right)-b\left(8a^3+6a^2b+6ab^2+b^3\right)\)
\(=a^4+6a^3b+6a^2b^2+8ab^3-8a^3b-6a^2b^2-6ab^3-b^4\)
\(=a^4+6a^3b+8ab^3-8a^3b-6ab^3-b^4\)
\(a\left(a+2b\right)^3-b\left(2a+b\right)^3\)
\(=a\left(a^3+6a^2b+12ab^2+8b^3\right)-b\left(8a^3+12a^2b+6ab^2+b^3\right)\)
\(=a^4+6a^3b+12a^2b^2+8ab^3-8a^3b-12a^2b^2-6ab^3-b^4\)
\(=a^4-2a^3b+2ab^3-b^4\)
\(=\left(a^2-b^2\right)\left(a^2+b^2\right)-2ab\left(a^2-b^2\right)\)
\(=\left(a^2-b^2\right)\left(a^2-2ab+b^2\right)\)
\(=\left(a+b\right)\left(a-b\right)^3\)
b) x^8+x^4+1
=x^8-x^2+x^4-x+x^2+x+1
=x^2(x^6-1)+x(x^3-1)+(x^2+x+1)
=x^2[(x^3)^2-1]+x(x^3-1)+(x^2+x+1)
=x^2(x^3-1)(x^3+1)+x(x^3-1)+(x^2+x+1)
=x^2(x-1)(x^2+x+1)(x^3+1)+x(x^3-1)+(x^2+x+1)
=x^2(x-1)(x^2+x+1)(x^3+1)+x(x-1)(x^2+x+1)+(x^2+x+1)
=(x^2+x+1)[x^2(x-1)(x^3+1)+x(x-1)+1]
=(x^2+x+1)(x^6+x^3-x^5-x+1)
dung thi tick cho minh nha minh thu may tinh roi
\(\left(2a+3\right)\left(2a+3\right)y+\left(2a+3\right)\)
\(=\left(2a+3\right)[y\left(2a+3\right)+1]\)
\(=\left(2a+3\right)\left(2ay+3y+1\right)\)
\(\left(a-b\right)x+\left(b-a\right)y-\left(a-b\right)\) (Sửa đề)
\(=\left(a-b\right)x-\left(a-b\right)y-\left(a-b\right)\)
\(=\left(a-b\right)\left(x-y-1\right)\)
\(\Leftrightarrow\left(a+b\right)^2+2\left(a+b\right)+1=\left(a+b+1\right)^2\)
x^3-x+6=x^3+2x^2-2x^2-4x+3x+6=x^2.(x+2)-2x.(x+2)+3.(x+2)=(x^2-2x+3).(x+2)