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\(1,\\ 1,=15\left(x+y\right)\\ 2,=4\left(2x-3y\right)\\ 3,=x\left(y-1\right)\\ 4,=2x\left(2x-3\right)\\ 2,\\ 1,=\left(x+y\right)\left(2-5a\right)\\ 2,=\left(x-5\right)\left(a^2-3\right)\\ 3,=\left(a-b\right)\left(4x+6xy\right)=2x\left(2+3y\right)\left(a-b\right)\\ 4,=\left(x-1\right)\left(3x+5\right)\\ 3,\\ A=13\left(87+12+1\right)=13\cdot100=1300\\ B=\left(x-3\right)\left(2x+y\right)=\left(13-3\right)\left(26+4\right)=10\cdot30=300\\ 4,\\ 1,\Rightarrow\left(x-5\right)\left(x-2\right)=0\Rightarrow\left[{}\begin{matrix}x=2\\x=5\end{matrix}\right.\\ 2,\Rightarrow\left(x-7\right)\left(x+2\right)=0\Rightarrow\left[{}\begin{matrix}x=7\\x=-2\end{matrix}\right.\\ 3,\Rightarrow\left(3x-1\right)\left(x-4\right)=0\Rightarrow\left[{}\begin{matrix}x=\dfrac{1}{3}\\x=4\end{matrix}\right.\\ 4,\Rightarrow\left(2x+3\right)\left(2x-1\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=-\dfrac{3}{2}\\x=\dfrac{1}{2}\end{matrix}\right.\)
\(x^4+3x^3+12x-16\)
\(=x^4+4x^3+4x^2+16x-x^3-4x^2-4x-16\)
\(=x\left(x^3+4x^2+4x+16\right)-\left(x^3+4x^2+4x+16\right)\)
\(=\left(x-1\right)\left(x^3+4x^2+4x+16\right)\)
\(=\left(x-1\right)\left[x^2\left(x+4\right)+4\left(x+4\right)\right]\)
\(=\left(x-1\right)\left(x+4\right)\left(x^2+4\right)\)
x4 + x3 + 2x2 + x + 1
= (x4 + 2x2 + 1) + (x3 + x)
= (x2 + 1)2 + x (x2 + 1)
= (x2 + 1) ( x2 + 1 + x)
= (x2 + 1) (x + 1)2
\(\left(x-3\right)^4+\left(x-1\right)^4-16\)
\(=\left(x-3\right)^4+\left[\left(x-1\right)^2-4\right]\left[\left(x-1\right)^2+4\right]\)
\(=\left(x-3\right)^4+\left(x-1-2\right)\left(x-1+2\right)\left(x^2-2x+5\right)\)
\(=\left(x-3\right)^4+\left(x-3\right)\left(x+1\right)\left(x^2-2x+5\right)\)
\(=\left(x-3\right)\left(x^3-9x^2+27x-27\right)+\left(x-3\right)\left(x^3-2x^2+5x+x^2-2x+5\right)\)
\(=\left(x-3\right)\left(x^3-9x^2+27x-27\right)+\left(x-3\right)\left(x^3-x^2+3x+5\right)\)
\(=\left(x-3\right)\left(x^3-9x^2+27x-27+x^3-x^2+3x+5\right)\)
\(=\left(x-3\right)\left(2x^3-10x^2+30x-22\right)\)
\(=2\left(x-3\right)\left(x^3-5x^2+15x-11\right)\)
\(=2\left(x-3\right)\left(x^3-x^2-4x^2+4x+11x-11\right)\)
\(=2\left(x-3\right)\left[x^2\left(x-1\right)-4x\left(x-1\right)+11\left(x-1\right)\right]\)
\(=2\left(x-3\right)\left(x-1\right) \left(x^2-4x+11\right)\)