Question

证明(x+1)(x+3)(x+5)(x+7)+15=(x^2+8x)^2+22(x^2+8x)+120

Answer 1

证明：(x+1)(x+3)(x+5)(x+7)+15 =[(x+1)(x+7)]*[(x+3)(x+5)]+15 =[(x^2+8x)+7)]*[(x^2+8x)+15)]+15 =(x^2+8x)^2+15(x^2+8x)+7(x^2+8x)+105+15 =(x^2+8x)^2+22(x^2+8x)+120