因式分解3a^2+6ab+3b^2 a^2b-6ab+9b (a+b)^2-14(a+b)+49 (p-4)(p+1)+3p

题目

因式分解3a^2+6ab+3b^2 a^2b-6ab+9b (a+b)^2-14(a+b)+49 (p-4)(p+1)+3p

答案

3a^2+6ab+3b^2
=3(a²+2ab+b²)
=3(a+b)²
a^2b-6ab+9b
=b(a²-6a+9)
=b(a-3)²
(a+b)^2-14(a+b)+49
=(a+b-7)²
(p-4)(p+1)+3p
=p²-3p-4+3p
=p²-4
=(p+2)(p-2)