Question

分解因式(a^2+5a+3)(a^2+5a-2)-6 x^2+4xy+4y^2+4x+8y+3 (x+3)(x^2-1)

Answer 1

(a^2+5a+3)(a^2+5a-2)-6

设a²＋5a=A

原式=(A＋3)(A－2)－6

=A²＋A－6－6

=A²＋A－12

=(A＋4)(A－3)

再把a²＋5a=A代入

原式= (A＋4)(A－3)

=(a²＋5a＋4)(a²＋5a－3)

=(a＋1)(a＋4)(a²＋5a－3)

x^2+4xy+4y^2+4x+8y+3

=[x²＋2×2xy＋(2y)²]＋(4x＋8y)＋3

=(x＋2y)²＋4(x＋2y)＋3

=(x＋2y＋1)(x＋2y＋3)

(x+3)(x^2-1)(x+5)-20

=(x＋3)(x＋1)(x－1)(x＋5)-20

=(x²＋4x＋3)(x²＋4x－5)－20

=(x²＋4x)²－2(x²＋4x)－15－20

=(x²＋4x)²－2(x²＋4x)－35

=(x²＋4x－7)(x²＋4x＋5)