Question

因式分解的问题

(m^2-m)x^2-(2m^2-1)x+m(m+1)

(2x-3a)(2x-a)(x+5a)(x+15a)-23a^2x^2

答案和过程噢都写一下哦.谢谢啦

Answer 1

因式分解的问题

(m^2-m)x^2-(2m^2-1)x+m(m+1) (十字相乘法)
=(mx-m-1)(mx-x-m)
(2x-3a)(2x-a)(x+5a)(x+15a)-23a^2x^2 (分组分解法)
=[(2x-3a)(x+15)][(2x-a)(x+5a)]-23a^x^
=[(2x^-15a^)+7ax][(2x^-15a^)+29ax]-23a^x^
=(2x^-15a^)^+36(2x^-15a^)ax+180a^x^
=(2x^-15a^+30ax)(2x^-15a^+6ax)

Answer 2

(m^2-m)x^2-(2m^2-1)x+m(m+1)
= m(m-1)x^2 -(2m^2-1)x +m(m+1)
= (mx-(m+1))((m-1)x-m)
=(mx-m-1)(mx-x-m)

(2x-3a)(2x-a)(x+5a)(x+15a)-23a^2x^2
=[(2x-3a)(x+5a)][(2x-a)(x+15a)]-23a^2x^2
=[(2x^2-15a^2)+7ax][(2x^2-15a^2)+29ax]-23a^2x^2
=(2x^-15a^)^2+36(2x^2-15a^2)ax+180a^2x^2
=(2x^2-15a^2+30ax)(2x^2-15a^2+6ax)