Question

因式分解（1）a²（a-b）²-b²（a-b）（a-b）

（2）（x+y+z）²-（x-y-z）² （3）（x+y）²-14（x+y）+49 （4）a²b²-0.01 （5）x²y-2xy²+y³ （6）16-（2a+3b）² （7）（a²+4）²-16a²

Answer 1

解
a²(a-b)²-b²(a-b)(a-b)
=(a-b)²(a²-b²)
=(a-b)²(a-b)(a+b)
=(a-b)³(a+b)

(x+y+z)²-(x-y-z)²
=[(x+y+z)+(x-y-z)][(x+y+z)-(x-y-z)]
=(2x)(2y+2z)
=4x(y+z)

(x+y)²-14(x+y)+49
=[(x+y)-7]²
=(x+y-7)²

a²b²-0,01
=(ab)²-0.1²
=(ab-0,1)(ab+0,1)

x²y-2xy²+y³
=y(x²-2xy+y²)
=y(x-y)²

16-(2a+3b)²
=4²-(2a+3b)²
=(4+2a+3b)(4-2a-3b)

(a²+4)²-16a²
=(a²+4)²-(4a)²
=(a²-4a+4)(a+4a+4)
=(a-2)²(a+2)²