\(\left(x^8-2x^4y^4+y^8\right):\left(x^2+y^2\right)\)

\(=\left(x^4-y^4\right)^2:\left(x^2+y^2\right)\)

\(=\left(x^2-y^2\right)^2\left(x^2+y^2\right)^2:\left(x^2+y^2\right)\)

\(=\left(x^2-y^2\right)^2\left(x^2+y^2\right)\)

Mẫu câu đầu 

\(4x^2+4x-5=4x^2+4x+1-6\)

\(=4\left(x^2+x+\frac{1}{4}\right)-9\)

\(=4\left(x^2+2.\frac{1}{2}.x+\frac{1}{4}\right)-6\)

\(=4\left(x+\frac{1}{2}\right)^2-6\ge-6\)

Vậy Min A=-6 dấu bằng xảy ra khi và chỉ khi \(x+\frac{1}{2}=0\Leftrightarrow x=-\frac{1}{2}\)

a)ab(a+b)-bc(b+c)+ac(a-c)

=ab(a+b)-bc(b+c)+ac\([\left(a+b\right)-\left(b+c\right)]\)

=ab(a+b)-bc(b+c)+ac(a+b)-ac(b+c)

=(a+b)(ab+ac)-(b+c)(bc+ac)

=(a+b)a(b+c)-(b+c)c(b+a)

=(a+b)(b+c)(a-c)

\(\left(a+b+c\right)\left(ab+bc+ca\right)-abc\)

\(=a^2b+abc+ca^2+ab^2+b^2c+abc+abc+bc^2+ac^2-abc\)

\(=a^2b+a^2c+ab^2+b^2c+c^2a+bc^2+ac^2+2abc\)

\(=\left(a^2b+ba^2+abc\right)+\left(b^2c+c^2b+abc\right)+\left(ac^2+ca^2\right)\)

\(=ab\left(a+b+c\right)+bc\left(a+b+c\right)+ac\left(a+c\right)\)

\(=\left(a+b+c\right)\left(ab+bc\right)+ac\left(a+c\right)\)

\(=b.\left(a+b+c\right)\left(a+c\right)+ac\left(a+c\right)\)

\(=\left(a+c\right)\left(ab+b^2+bc+ac\right)\)

\(=\left(a+c\right)\left[b.\left(a+b\right)+c.\left(a+b\right)\right]\)

\(=\left(a+c\right)\left(a+b\right)\left(b+c\right)\)

mk ko bt

1/\(\left(x^2-6x+15\right):\left(x-3\right)\)

Đặt cột dọc ta được x-3 dư 6 

2/a/\(p=\left(x+1\right)^3+\left(x+1\right)\left(6-x^2\right)-12\)

\(=x^3+3x^2+3x+1+6x-x^3+6-x^2-12\)

\(=2x^2+9x-11\)

b/thay x = -1/2 ta đc \(2.-\left(\frac{1}{2}\right)^2+9.-\frac{1}{2}-11\)

\(=\frac{1}{2}+\left(-\frac{9}{2}\right)-11\)

\(=\left(-15\right)\)

\(x^2-2xy+y^2+3x-3y-0\)0 = \(\left(x-y\right)^2+3\left(x-y\right)\)= \(\left(x-y\right)\left(x-y+3\right)\)

x²-2xy+y²+3x-3y=0

\(\Leftrightarrow\left(x-y\right)^2+3\left(x-y\right)=0.\)

\(\Leftrightarrow\left(x-y\right)\left(x-y+3\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x-y=0\\x-y+3=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=y\\x=y-3\end{cases}}}\)

CMR: a^5 - a chia hết cho 30 với mọi số nguyên a