Question

用因式分解方法做简便计算一 .12.5^2－12.5×5＋6.25 二.21.5^2－3×21.5＋1.5^2－100

Answer 1

需要用到一些公式：a^2-2ab+b^2=(a-b)^2,a^2-b^2=(a+b)(a-b),ab+ac+ad=a(b+c+d)

1) 12.5^2-12.5*5+6.25

=12.5^2-2*12.5*2.5+2.5^2

=(12.5-2.5)^2

=10^2

=100

2) 21.5^2-3*21.5+1.5^2-100

=21.5^2-2*21.5*1.5+1.5^2-100

=(21.5-1.5)^2-100

=20^2-10^2

=(20+10)(20-10)

=30*10

=300

3) 125*0.45-12.5*6.7+1.25*122

=12.5*4.5-12.5*6.7+12.5*12.2

=12.5*(4.5+12.2-6.7)

=12.5*10

=125