因式分解9(a-b)²+12(a²-b²)+4(a+b)²

因式分解9(a-b)²+12(a²-b²)+4(a+b)²
因式分解9(a-b)²+12(a²-b²)+4(a+b)²

因式分解9(a-b)²+12(a²-b²)+4(a+b)²
=9a²-18ab+9b²+12a²-12b²+4a²+8ab+4b²
=25a²-10ab+b²
=(5a-b)²

9(a-b)²+12(a²-b²)+4(a+b)²
=[3(a-b)]^2+2x[3(a-b)]x[2(a+b)]+[2(a+b)]^2
=[3(a-b)+2(a+b)]^2
=(5a-b)^2

9a²-18ab+b²+12a²-12b²+4a²+8ab+4b²
= 25a²-10ab+4b²
=（5a-2b)²

9(a-b)²+12(a²-b²)+4(a+b)²
=9（a^2+b^2-2ab)+12a^2-12b^2+4(a^2+b^2+2ab)
=25a^2+b^2-10ab
=(5a-b)^2

原式＝[3﹙a－b﹚]²＋2×3×2﹙a－b﹚﹙a＋b﹚＋[2﹙a＋b﹚]²
＝[3﹙a－b﹚＋2﹙a＋b﹚]²＝﹙3a－3b＋2a＋2b﹚²＝﹙5a－b﹚²