Question

先提公因式再利用公式对下列各式进行因式分解: ①2x³y–2xy³ ②a∧nb

先提公因式再利用公式对下列各式进行因式分解:
①2x³y–2xy³ ②a∧nb∧2n–a∧c²
③3(a＋b)²–27c²④a²(a–b)–b²(a–b)
⑤x²(a–b)＋y²(b–a)⑥3m(2x–y)²–3mn² ⑦(y–1)＋x²(1–y)
⑧32(x+y)²–50(x–y)²

Answer 1

①=2xy(x² - y²)
=2xy(x+y)(x-y)
②不能提取公因式吧
③=3[(a+b)² - 9c²]
=3(a+b+3c)(a+b-3c)

追答

④=(a-b)(a² - b²)
=(a-b)(a-b)(a+b)
=(a+b)(a-b)²
⑤=x²(a-b) - y²(a-b)
=(a-b)(x² - y²)
=(a-b)(x+y)(x-y)
⑥=3m[(2x-y)² - n²]
=3m(2x-y+n)(2x-y-n)
(7)=(y-1) - x²(y-1)
=(y-1)(1-x²)
=(y-1)(1+x)(1-x)
(8)=2[16(x+y)² - 25(x-y)²]
=2[4(x+y)+5(x-y)][4(x+y)-5(x-y)]
=2(4x+4y+5x-5y)(4x+4y-5x+5y)
=2(9x-y)(9y-x)