a) $x^{4}$+2x³-4x-4
= $x^{4}$-2x²+2x³-4x+2x²-4
= x²(x²-2)+2x(x²-2)+2(x²-2)
= (x²-2)(x²+2x+2)
c) (x-5)²+(x+5)-(5-x)(2x+1)
= x²-10x+25+x+5-10x-5+2x²+x
= 3x²-18x+25
d) (a-b)(a+2b)-(b-a)(2a-b)-(a-b)(a+3b)
= (a-b)(a+2b)+(a-b)(2a-b)-(a-b)(a+3b)
= (a-b)(a+2b+2a-b-a-3b)
= (a-b)(2a-2b)
= 2(a-b)(a-b)
= 2(a-b)²