Question

因式分解！！！急急急谢谢！！！！！！！

1、1-m+1/4m^2
2、4x^2+20xy+25y^2
3、x（^2+4）^2-16x^2
4、x^4-2x^2+1
利用因式分解计算：1.1/2×3.7^2-3.7×2.7+1/2×2.7^2
2.9.9^2+9.9×0.2+0.01

Answer 1

1、1-m+1/4m^2=(1-1/2m)^2
2、4x^2+20xy+25y^2=(2x+5y)^2
3、(x^2+4）^2-16x^2=(x^2+4+4x)(x^2+4-4x)=(x+2)^2(x-2)^2
4、x^4-2x^2+1=(x^2-1)^2=(x+1)^2(x-1)^2
利用因式分解计算：
1.1/2×3.7^2-3.7×2.7+1/2×2.7^2
=1/2×(3.7^2-2×3.7×2.7+2.7^2)
=1/2×(3.7-2.7)^2
=1/2×1^2
=1/2
2.9.9^2+9.9×0.2+0.01
=(9.9+0.1)^2
=10^2
=100

追问

为什么这么做 原因能说出来吗

Answer 2

1.1-m+1/4m^2=(1-1/2m)^2
2.4x^2+20xy+25y^2=(2x+5y)^2
3.x（^2+4）^2-16x^2=x^4+8x^2+16-16x^2=x^4-8x^2+16=(x^2-4)^2=(x-2)^2(x+2)^2
4.x^4-2x^2+1=(x^2-1)^2=(x-1)^2(x+1)^2

1.1/2×3.7^2-3.7×2.7+1/2×2.7^2=1/2(3.7-2.7)^2=1/2*1^2=1/2
2.9.9^2+9.9×0.2+0.01=(9.9+0.1)^2=10^2=100

Answer 3

=1/2*(3.7^2-2*3.7*2.7+2.7^2)=1/2*(3.7-2.7)^=1/2
=9.9^2+9.9*0.2+0.1^2=(9.9+0.1)^2=100