maths 因式分解

a.
a^2 (b+1)^2 -16
=[a(b+1)]^2-4^2
=[(ab+a)-4][(ab+a)+4]
=(a+ab-4)(a+ab+4)

b.
(b - 1)^2 - 10(b - 1) + 25
=[(b-1)-25]^2
=(b-26)^2

c.
6p^2 + 19p - 7
=(3p-1)(2p+7)

d.
2ox^2 + 44xy - 15y^2
=(10x-3y)(2x+5y)

e.
-6m^2 + 46mn - 60n^2
=-2(3m^2-23mn+30^2)
=-2(m-6n)(3m-5n)

f.
(2a + b)(2a - b) - 4a^2+b^2
=(2a+b)(2a-b)-(2a-b)(2a+b)
=0

g.
a^3 + b^3 - a^2b - ab^2
=a^3-ab^2+b^3-a^2b
=a(a^2-b^2)+b(b^2-a^2)
=a(a^2-b^2)-b(a^2-b^2)
=(a^2-b^2)(a-b)
=(a+b)(a-b)(a-b)
=(a+b)(a-b)^2

a. (ab+a)^2-16 = (ab+a-4)(ab+a+4)
b. (b-1-5)^2 = (b-6)^2 = b^2-12b+36
c. (3p-1)(2p+7)
d. (10x-3y)(2x+5y)
e. 2(3m-5n)(1m-6n)
f. (2a-1)^2-b^2 = (2a-1+b)(2a-1-b)
g. (a+b)(a^2-ab+b^2)-ab(a+b) = (a+b)(a-b)^2