Question

因式分解，利用因式分解简便计算.要有过程

(1)11^2+39^2+13×66
(2)（x+2）（x+4）+x^2-4
(3)1/4x+x^3-x^2
(4)m^4-2(m^2-1/2)
(5)9(a-b)^2-30(a^2-b^2)+25(a+b)^2

Answer 1

(1)11^2+39^2+13×66
=11^2+（3×13）^2+13×3×2×11
=(11+3×13)^2
=50^2
=2500
(2)（x+2）（x+4）+x^2-4
=（x+2）（x+4）+(x+2）（x-2)
=(x+2)[(x+4)+(x+2)]
=(x+2)(2x+6)
=2(x+2)(x+3)
(3)1/4x+x^3-x^2
=1/4x(1+4x^2-4x)
=1/4x(2x-1)^2
(4)m^4-2(m^2-1/2)
=m^4-2m^2+1
=(m^2-1)^2
(5)9(a-b)^2-30(a^2-b^2)+25(a+b)^2
=[3(a-b)-5(a+b)]^2
=(2a+8b)^2
=4(a+4b)^2