Question

因式分解

(m²-m)(m²-m+1)-26
（a²-3）（a²+7）+16
（x+1)(x+3)(x+5)(x+7)+15
速度

Answer 1

(m²-m)(m²-m+1)-26
=(m²-m)²+(m²-n)-26
=(m²-m)²+(m²-n)+1/4-1/4-26
=(m²-m+1/2)²-105/4
=(m²-m+1/2)²-(√105/2)²
=(m²-m+1/2+√105/2)(m²-m+1/2-√105/2)

（a²-3）（a²+7）+16
=(a²+2-5)(a²+2+5)+16
=(a²+2)²-25+16
=(a²+2)²-9
=(a²+2)²-3²
=(a²+2+3)(a²+2-3)
=(a²+5)(a²-1)

（x+1)(x+3)(x+5)(x+7)+15
=(x+1)(x+7)(x+3)(x+5)+15
=(x²+8x+7)(x²+8x+15)+15
=(x²+8x+11-4)(x²+8x+11+4)+15
=(x²+8x+11)²-16+15
=(x²+8x+11)²-1²
=(x²+8x+11+1)(x²+8x+11-1)
=(x²+8x+12)(x²+8x+10)
=(x+2)(x+6)(x+4+√6)(x+4-√6)