Question

因式分解：第一题9m^2-25n^4 第二题（x+y)^4-(x-y)^4 三题2ab-(ab)^2-1+c 四题abc

Answer 1

9m^2-25n^4

=(3m+5n)(3m-5n)

（x+y)^4-(x-y)^4

={(x+y)^2+(x-y)^2}{(x+y)^2-(x-y)^2}

=(2x^2+2y^2)4xy

=8xy(x^2+y^2)

2ab-(ab)^2-1+c^2

=c^2-(ab-1)^2

=(c+ab-1)(c-ab+1)

ab(c^2+d^2)+cd(a^2+b^2)

=abc^2+abd^2+cda^2+cdb^2

=abc^2+cdb^2+abd^2+cda^2

=bc(ac+bd)+ad(bd+ac)

=(bd+ac)(ad+bc)