\(x^4+4\)
\(=x^4+4x^2+4-4x^2\)
\(=\left[\left(x^2\right)^2+2.x^2.2+2^2\right]-4x^2\)
\(=\left(x^2+2\right)^2-\left(2x\right)^2\)
\(=\left(x^2+2-2x\right)\left(x^2+2+2x\right)\)
\(\text{a) }3x-7x+2\\ \\=2-4x\\ \\=2\left(1-2x\right)\)
\(\text{b) }x^4+4\\ \\=x^4+4+4x^2-4x^2\\ \\=\left(x^4+4x^2+4\right)-4x^2\\ \\=\left(x^2+2\right)^2-\left(2x\right)^2\\ \\=\left(x^2+2+2x\right)\left(x^2+2-2x\right)\\ \)
\(\text{c) }4x-8y=4\left(x-2y\right)\)
\(\text{d) }x^3-x^2y-x+y\\ \\=\left(x^3-x^2y\right)-\left(x-y\right)\\ \\=x^2\left(x-y\right)-\left(x-y\right)\\ =\left(x-y\right)\left(x^2-1\right)\\ \\=\left(x-y\right)\left(x-1\right)\left(x+1\right)\)
\(3x-7x+2\)
\(=x\left(3-7\right)+2\)
\(=-4x+2\)
\(=2\left(-2x+1\right)\)
\(x^3-x^2y-x+y\)
\(=\left(x^3-x^2y\right)-\left(x-y\right)\)
\(=x^2\left(x-y\right)-\left(x-y\right)\)
\(=\left(x-y\right)\left(x^2-1\right)\)
\(=\left(x-y\right)\left(x-1\right)\left(x+1\right)\)
x4+4
=x4+4x2+4-4x2
=(x2+2)2-4x2
=(x2+2-2x)(x2+2+2x)
x3- x2y-x+y
=(x3-x2y)-(x-y)
=x2(x-y)-(x-y)
=(x-y)(x2-1)
4x-8y
=4(x-2y)
3x-7x+2
=-4x+2
=-2(x+1)
