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\(a,a^3-7a-6\)
\(\Leftrightarrow a^3+a^2-a^2-a-6a-6\)
\(\Leftrightarrow a^2\left(a+1\right)-a\left(a+1\right)-6\left(a+1\right)\)
\(\Leftrightarrow\left(a+1\right)\left(a^2-a-6\right)\)
\(\left(x+1\right)\left(x+2\right)\left(x-3\right)\)
\(b,a^3+4a^2-7a-10\)
\(\Leftrightarrow a^3+5a^2-a^2-5a-2a-10\)
\(\Leftrightarrow a^2\left(a+5\right)-a\left(a+5\right)-2\left(a+5\right)\)
\(\Leftrightarrow\left(a+5\right)\left(a+1\right)\left(a-2\right)\)
\(d,\left(a^2+a\right)^2+4\left(a^2+a\right)-12\)
Đặt a^2+a=y ta có
y^2+4y-12=(y+6)(y-2)
<=> (a^2+a+6)(a^2+a-2)
<=> (a^2+a+6)(x-1)(x+2)
nhân tung \(\left(a^2-b\right)\left(b^2-c\right)\left(c^2-a\right)\) ra đề rồi viết ngược lại =.=
a)\(ab\left(a+b\right)-bc\left(b+c\right)+ac\left(a-c\right)\)
\(=\left(a+b\right)\left(b+c\right)\left(a-c\right)\)
b)\((a+b)(a^2-b^2)+(b+c)(b^2-c^2)+(c+a)(c^2-a^2)\)
\(=\left(a-b\right)\left(b-c\right)\left(c-a\right)\)
c)\(a^2b^2(a-b)+b^2c^2(b-c)+c^2a^2(c-a)\)
\(=\left(a-b\right)\left(a-c\right)\left(b-c\right)\left(ab+bc+ca\right)\)
d)\(a^4(b-c)+b^4(c-a)+c^4(a-b)\)
\(=\left(a-b\right)\left(b-c\right)\left(c-a\right)\left(a^2+b^2+c^2+ab+bc+ca\right)\)
a) \(4a^3b^3c^2x+12a^3b^4c^2-16a^4b^5cx\)
\(=4a^3b^3c\left(cx+3bc-4ab^2x\right)\)
b) \(\left(b-2c\right)\left(a-b\right)-\left(a+b\right)\left(2c-b\right)\)
\(=\left(b-2c\right)\left(a-b+a+b\right)=2a\left(b-2c\right)\)
c) \(3a\left(a+5\right)-2\left(5+a\right)=\left(a+5\right)\left(3a-2\right)\)
d) \(\left(x+1\right)^2-3\left(x+1\right)=\left(x+1\right)\left(x+1-3\right)\)