因式分解(x²+4x+3)（x²+12x+35)+15

因式分解(x²+4x+3)（x²+12x+35)+15
因式分解(x²+4x+3)（x²+12x+35)+15

因式分解(x²+4x+3)（x²+12x+35)+15
式子中^2表示平方
(x^2+4x+3)(x^2+12x+35)+15
=(x+1)(x+3)(x+5)(x+7)+15
=(x+1)(x+7)(x+5)(x+3)+15
=(x^2+8x+7)(x^2+8x+15)+15
=(x^2+8x)^2+22(x^2+8x)+105+15
=(x^2+8x)^2+22(x^2+8x)+120
=(x^2+8x+10)(x^2+8x+12)
=(x+3)(x+5)(x+2)(x+6)

式子中^2表示平方
(x^2+4x+3)(x^2+12x+35)+15
=(x+1)(x+3)(x+5)(x+7)+15
=(x+1)(x+7)(x+5)(x+3)+15
=(x^2+8x+7)(x^2+8x+15)+15
=(x^2+8x)^2+22(x^2+8x)+105+15
=(x^2+8x)^2+22(x^2+8x)+120
=(x^2+8x+10)(x^2+8x+12)
=(x+3)(x+5)(x+2)(x+6)

原式=（x+1）（x+3）（x+5）（x+7）+15
=（x²+8x+7）（x²+12x+15）+15
令t=x²+8x
原式=（t+7）（t+15)+15=t²+22t+120=(t+10)(t+12)
=(x²+8x+10)(x²+8x+12)
=(x+2)(x+6)(x²+8x+10)
7月v8